The worry is this. Jason thinks that when the stakes are high, it's harder to know. But stakes aren't just a feature of an individual at a time; stakes are high for certain propositions when the truth or falsehood of those propositions make a big difference. It's possible to be such that the stakes for p are high, but the stakes for q are low. For example, it may be very important to Hannah and her wife Sarah whether the bank is open tomorrow, but not at all important to them whether it will rain tomorrow. In such a case, they would need to meet more exacting 'standards' in order to know about the bank than they would to know about the rain. That's a little bit counterintuitive, but only in the way that pragmatic encroachment is generally a little bit counterintuitive.
But here's what might be a deeper problem. Suppose someone is in a situation like the one just mentioned -- the stakes for p are high, but the stakes for q are low -- but where the subject knows that if q, then p. If so, then it's easy to know q, but hard to know p; but it looks like anyone who knows q could easily infer p. Closure plus the possibility of a case with this structure looks like they entail that the stakes-sensitive view can't be right.
Do we have to say such cases are possible? I don't see anything that forces us to, but certain cases are very naturally described in that way. Suppose Hannah and Sarah have an important bill, as per the standard high-stakes bank case; it's very important to them whether the bank will be open on Saturday. Suppose also that they have a friend Franklin who is a bank teller, and they have some small interest in whether he will be at the bank on Saturday. Here, however, the stakes are low -- nothing much hangs on whether they're correct about Franklin's location on Saturday. Assume that they have a good enough position for arbitrary strong knowledge standards for the proposition that Franklin will be at the bank only if it is open. So we have:
- p: The bank is open Saturday
- q: Franklin is at the bank Saturday
- The stakes for p are high
- The stakes for q are low
- Everyone knows that if q, then p.
If Hannah and Sarah have a middling epistemic position with respect to q, then it looks like they're in a position to know q, but not to know p. But this violates closure.
Might Jason say that in such a case, the high stakes for p force the stakes up for q as well? He might, but it seems like a pretty strange thing to say. Intuitively, it doesn't matter to them much at all whether Franklin is at work on Saturday. Their bill situation has nothing to do with Franklin. Maybe we can wrap our heads around the idea that the bill makes it harder to know that the bank is open -- but can it really make it harder to know where their friends are?