I’ve been thinking again about the issues about knowledge justified belief and practical interests that I explored a bit in “this old paper”:http://brian.weatherson.org/cwdwpe.pdf. 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_.