Here’s an abstract version of one of the train puzzles I was describing a couple of posts below. What’s interesting here is whether these cases pose a problem for Fantl and McGrath’s principle (PC).

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

Let p be some (true) proposition about the date of a moderately famous historical event, and S a subject with a slightly fuzzy recollection that p is in fact true. (Assume S’s recollection is not Gettierised, her memory that p is caused by p in a perfectly acceptable way, but she could potentially doubt that p.) A is a bet that pays $1 if p is true, and leads to a loss determined by the formula below.

Now the complications start. Let q, r and t be three mutually exclusive and jointly exhaustive propositions. Our subject S believes q, but all her evidence points towards r, although in fact t is true. Now here’s the formula for how much A costs if p is false.

If q is true, A costs $3
If r is true, A costs $200
If t is true, A costs $2

Assume (as seems reasonable) that given r, S does not find this a very good bet. But she does find it a good bet given q and given t. That is, she’s prepared to bet on p at 2 or 3 to 1, but not at 200 to 1, which is smart given her evidence. Since she thinks q is true, she takes the bet (and wins a dollar).

I think it’s plausible (not mandatory but plausible) to say that she is justified in the circumstances in believing p, but not rational in acting as she does as if p is true. That would be a counterexample to (PC). Moreover, since t is true so this bet is actually a low-stakes bet, we can believe this even if we think that whether one has a justified belief is sensitive to pragmatic matters.

I’m not actually committed to this being a counterexample, and in fact my own position on the example is a little more convoluted that I’d like. But I think it’s a tricky case which it’s worth getting clear about.

Any thoughts?