In “this paper”:http://brian.weatherson.org/cwdwpe.pdf, I offered the following analysis of belief.

bq. S believes that p iff for any* A, B, S prefers A to B simpliciter iff S prefers A to B conditional on p.

The * on any is to note that the quantifier is restricted in all sorts of ways. One of the restrictions is senstive to S’s interests, so this becomes a version of interest-relative invariantism about belief. And if we assume that belief is required for knowledge we get (with some other not too controversial premises) interest-relative invariantism about knowledge.

I now think this wasn’t quite the right analysis. But I don’t (yet!) want to take back any of the claims about the restrictions on any. Rather, I think I made a mistake in forcing everything into the mold of preference. What I should have said was something like the following.

bq. S believes that p iff for any* issue, S’s attitudes simpliciter and her attitudes conditional on p match.

Here are some issues, in the relevant sense of issue. (They may be the only kind, though I’m not quite ready to commit to that.)

* Whether to prefer A to B
* Whether to believe q
* What the probability of q is

Previously I’d tried to force the second issue into a question about preferences. But I couldn’t find a way to force in the third issue as well, so I decided to retreat and try framing everything in terms of issues.

Adding questions about probability to the list of issues allows me to solve a bunch of tricky problems. It is a widely acknowledged point that if we have purely probabilistic grounds for being confident that p, we do not take ourselves to (unconditionally) believe that p, or know that p. On the other hand, it hardly seems plausible that we have to assign p probability 1 before we can believe or know it. Here is how I’d slide between the issues.

If I come to be confident in p for purely probabilistic reasons (e.g. p is the proposition that a particular lottery ticket will lose, and I know the low probability that that ticket will win) then the issue of p’s probability is live. Since the probability of p conditional on p is 1, but the probability of p is not 1, I don’t believe that p. More generally, when the probability of p is a salient issue to me, I only believe p if I assign p probability 1.

However, when p’s probability is not a live issue, I can believe that p is true even though I (tacitly) know that its probability is less than 1. That’s how I can know where my car is, even though there is some non-zero probability that it has been stolen/turned into a statue of Pegasus by weird quantum effects. Similarly I can know that the addicted gambler when end up impoverished, though if pushed I would also confess to knowing there is some (vanishingly small) chance of his winning it big.