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February 24th, 2008

Knowledge, Justified Belief and Practical Interests

I’ve been thinking again about the issues about knowledge justified belief and practical interests that I explored a bit in this old paper. In that paper I have a rather complicated example that’s meant to show that a principle Jeremy Fantl and Matthew McGrath endorse, namely (PC) is false. Here is the principle.

(PC) S is justified in believing that p only if S is rational to prefer as if p.

The rough outline of why (PC) is wrong is that whether one is rational to prefer as if p might depend not only on whether one has justified attitudes towards p, but on whether one’s other attitudes are justified. Here is one example in which that distinction matters.

S justifiably has credence 0.99 in p. She unjustifiably has credence 0.9999 in q. (She properly regards p and q are probabilistically independent.) In fact, given her evidence, her credence in q should be 0.5.

S is offered a bet that pays $1 if _p_v_q_ is true, and loses $1000 otherwise. Assume S has a constant marginal utility for money. It is irrational for S to prefer to take the bet. Given her evidence, it has a negative expected value. Given her (irrational) beliefs, it has a positive expected value, but if she properly judged the evidence for q, then she would not take the bet.

Of course, given p the bet is just a free grant of $1, so she should take it.

So this is a case where it is not rational to prefer as if p. She should prefer to decline the bet, but to accept the bet given p.

If we accept (PC), it follows that S is not justified in believing p. But this conclusion seems wrong. S’s credence in p is perfectly justified. And on any theory of belief that seems viable around here, S’s credence in p counts as a belief. (On my preferred view, S believes p iff she prefers as if p. And she does. The main rival to this view is the “threshold view”, where belief requires a credence above the threshold. And the usual values for the threshold are lower than 0.99.)

So this is a counterexample to (PC). In a recent paper, Fantl and McGrath defend a weaker principle, namely (KA).

(KA) S knows that p only if S is rational to act as if p.

Is this case a counterexample to (KA) as well? (Assume that p is true, so the agent could possibly know it.) I don’t believe that it is a counterexample. I think the things that an agent knows are the things she can use to frame a decision problem. If the agent knows p, then the choice between taking or declining the bet just is the choice between taking a dollar and refusing it. So she should take the bet. This would be irrational, so that must be the wrong way to frame the bet. Hence she doesn’t know that p.

The upshot of this is that these practical cases give us a new kind of counterexample to K = JTB. In the case I’ve described, the agent has a justified true belief that p, but does not know p.

Posted by Brian Weatherson in Uncategorized

3 Comments »

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3 Responses to “Knowledge, Justified Belief and Practical Interests”

  1. Jeremy Fantl says:

    Hi Brian,

    I’m interested in what condition you’d add to JTB+anti-Gettierish conditions in order to get a guarantee that when S knows that p S is rational to act as if that p. I assume it would be something like this:

    S knows that p only if S’s strength of epistemic position is sufficient to make it the case that S is rational to act as if p.

    (This is really just KA, but with it made explicit that knowledge makes S’s strength of epistemic position sufficient to make S rational to act as if p.)

    But what sorts of increases in S’s epistemic position would make it the case that S is rational to act as if p? Presumably, it would be changes that make S’s justified credence level higher. All these changes, it seems to me, will make it the case that S is more justified in believing that p. (That is, you don’t make S’s strength of epistemic position sufficient to make S rational to act as if p by making S unGettiered or by making p true.)

    So, it sounds to me like, for S to know that p, S must have a strength of justification for p that makes S rational to act as if p.

    Any degree of justification short of this won’t be the degree of justification S has to have in order to know. But if S has this degree of justification, then S has the degree of justification required to know: S has knowledge-level justification.

    But the original principle in our 2002 was just about knowledge-level justification (as stipulated in one of the footnotes). There’s an additional question whether knowledge-level justification is equivalent to plain-old justification in believing. We think it is (if justification is an obliging rather than just a permitting notion). But that’s a separate matter and independent of PC, which is just about knowledge-level justification and, it seems to me, still true.

    -Jeremy

  2. Brian Weatherson says:

    I think that if you don’t start with the idea that knowledge is factorisable, then it is hard to get this line of reasoning off the ground. It’s hard to even say what “knowledge-level justification” comes to. Maybe this will become clearer in what I say below.

    In the example I’ve described, S doesn’t need to increase their “epistemic position” in order to know that p. They simply need to get enough evidence for q that her credences in it are justified. Once they do that, they know p. That seems to imply that S does have a sufficient degree of justification for p in order to know it. So even if we interpret (PC) that way, this is still a counterexample.

    Now of course they could also come to know p by getting more evidence, i.e. by becoming justified in believing p to a higher degree.

    So should we say that her strength of justification is strong enough for knowledge or not? I’m not sure the question has a clean answer. Holding fixed her evidence for q, her strength of justification for p isn’t high enough. Holding fixed her credence in q, her strength of justification for p is high enough, but she has a “pragmatic defeater” insofar as that credence in q is not justified.

  3. Jeremy Fantl says:

    It’s a nice example, for sure, and I think it’s a very helpful clarification of what you were getting at in the original paper. One consequence that some people will think is bad news for both of us is that we can come to know p by getting evidence for clearly-probabilistically-independent q. That’s intuitively not so great, but it’s just a cost that may have to be borne, if the arguments for KA are strong enough.

    So, is her strength of justification for p enough for knowledge? Your worry seems to be that, perhaps what’s stopping me from knowing that p is my strength of justification, not for p, but for q. And we’ll agree that raising her justified credence for p would allow her to know that p and raising her justified credence for q would allow her to know that p.

    What follows from seems not that she does have knowledge-level for p, but that it is overdetermined that she doesn’t know. But one thing that is preventing her from knowing is her lack of justification for p.

    Consider the following case: suppose that she is in exactly the same epistemic position wrt both p and q. She is justified in having credence .99 in each, but has credence .9999 in both. Then she does not know either (on both our views). We’ll say that she has knowledge-level justification for neither because one thing stopping her from knowing p is her strength of justification for p and one thing stopping her from knowing q is her strength of justification for q.

    Your response in your posted example is that she lacks knowledge that p because of a lack of justification for q. This won’t be plausible in the revised example: it can’t be that what’s stopping her from knowing that p is her strength of justification for q and what’s stopping her from knowing q is her strength of justification for p. Perhaps what’s stopping her from knowing either is her strength of justification for p or perhaps what’s stopping her from knowing either is her strength of justification for q. But why make either p or q the preferred proposition? Why not say what seems most natural? Her justification for p in this case isn’t knowledge-level, because if it were higher, she’d know. Her justification for q isn’t knowledge-level, because if it were higher, she’d know. Likewise in your posted case: if her justification for p were higher, she’d know. So her justification for p isn’t knowledge-level. Yes, if her justification for q were higher, she’d know that p also. But that just means that, in a different case, her justification for p would be knowledge-level. And that’s just the view: what level of justification counts as knowledge-level can fluctuate with changes in what’s rational to do.

    Lastly, I’m not sure that unfactorisability is so important, here. The defense of PC doesn’t depend on knowledge being analyzable in any way. It just depends on it being the case that your knowing p in such a case entails that p have a certain degree of justification for you. Crucial to the individuation of the case is your lack of evidence for q. In that sort of case, that you know that p entails that you have a significantly higher degree of justification than .99.

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