It isn't true that all interest-invariant epistemologies are alike, but it is certainly true that every interest-relative theory is interest-relative in its own idiosyncratic way. In fact, there are at least four dimensions along which a theory can be interest-relative.I used to think (Weatherson, 2005) that interest-relativity in knowledge was to be explained by interest-relativity in belief, but I came to think that's not true (Weatherson, 2012). Some prominent defenders of interest-relativity in epistemology focus on practical interests -it's even there in the title of the book by Jason Stanley (2005) -but others of us think that theoretical interests matter too. At times Stanley writes as if interest-relativity means that there is an extra clause in the theory of knowledge for interests, but one need not think that. It could, for example, be that there is an interest-sensitive domain restriction on a quantifier in one of the clauses.But for present purposes, the key divide among interest-relative epistemologists is between those who think that stakes are relevant, and those who think odds are relevant. I think, following Mark Schroeder (2012), that it is odds that matter. The key examples here are ones where there is little cost to gambling and getting it wrong, but even less to gain by gambling and getting it right.So imagine that Ankita is walking to a restaurant she hasn't been to for a few months. She is stopped at the lights, reading baseball scores on her phone. She is almost, but not completely, certain that she should turn left at the next block, which indeed she should. If she had been wrong, she would have gone two blocks out of her way. She could avoid this risk by flipping from her baseball app to the map on her phone and checking the address, all of which she could do before the lights change. I say that in this circumstance, she doesn't know where the restaurant is. She should look up where it is, that's what maximises expected utility, but she needn't look up restaurants she knows the location of. So she doesn't know whether the restaurant is to her left or her right. Ankita's case is not a high-stakes one. Even on a cold Michigan Fall evening, the downside of walking two extra blocks is not that high. But unless she really really cares about those baseball scores she's browsing through, deciding not to flip over to the map is a gamble on the correctness of her plans at incredibly long odds. That's not because the stakes are high, but because the gain from gambling is low. This is a genuine case of interest-relativity though. The argument I just gave wouldn't go through if Ankita would have no disutility whatsoever from walking two blocks out of her way. (Maybe the exercise gain would completely outweigh the frustration.) In that case, perhaps she does know. But if the two block walk has many times the disutility of no longer browsing baseball scores, as it would in most realistic cases, her interests defeat her knowledge of the restaurant location.
