Consider an agent S who doesn’t know what her evidence is. If Williamson is right, then we are in S’s position all of the time. Assuming S is in a position where different evidence would justify different credences in some proposition p, the following three things can’t be true of S.

• Confirmation Awareness: S knows what the rational response is to some class of possible evidential input, and her actual evidence is in that class.
• Credal Awareness: S knows what her credence in p is.
• Rationality Awareness: S knows that she is responding rationally to her evidence.

Williamson thinks that cases like S are common. In any such case, one of the three awareness claims must fail. Which is most likely to fail? That is, for realistic versions of S, which of these three claims is actually false? I think this is relevant for thinking about the possibility of modelling some familiar and interesting cases, such as Sleeping Beauty, in terms of unknown evidence.

Thinking this through is interesting because it affects what we want to say about the applicability of Williamsonian ideas to everyday cases. Consider, for instance, the following toy example, modelled closely on some examples of Williamson.

An agent is in state S1, or state S2, or state S3. Right now they regard each state as equally probable. They are about to get some evidence. When they get that evidence, then whatever state they are in, they won’t know they are not in the adjoining state, and obviously they won’t know they aren’t in the state they are in. But that’s all they won’t know. So if they are in S1, they’ll know they are in S1 or S2. If they are in S3, they will know they are in S2 or S3. And if they are in S2, they won’t get any usable information.

The agent is actually in S1. What should their credence be that they are in S1? Answer: 1/2. Their evidence is that they are in S1 or S2, conditionalising on that leads to a probability of 1/2 that they are in S1. But note, for all the agent knows, they are in S2. And if they are in S2, then their evidence is consistent with S3. In that case, conditionalising on their evidence should lead to a probability of 1/3 that they are in S1.

There is something odd about the case. The agent can’t know (a) that the right thing to do when (and only when) their evidence is S1 or S2 is to have credence 1/2 in S1, (b) that their credence in S1 or S2 is 1/2 and (c) that they are doing the right thing . If they knew (a), (b) and (c), they’d be able to deduce that their evidence was S1 or S2, and from that they’d be able to deduce that they are in S1. But they can’t know any such thing. So one of (a), (b) and (c) fails. In realistic models of this kind of situation, which of them actually fails.

It seems to me easy enough to think of cases where Confirmation Awareness holds. In cases where there are only a few possible evidential inputs, or in cases where the initial credal distribution over possible outcomes is quite straightforward (perhaps because we’re concerned with the behaviour of a chance device with known chances) it can be quite clear how to conditionalise on various pieces of evidence. So while Confirmation Awareness sometimes fails, I think it often holds.

There is a simple argument that Credal Awareness can’t fail, at least for instrumentally rational agents. The agent can just arrange for themselves to be offered bets on p at various odds, and they can look and see which ones they accept. So they’ll know which credence they have. I think that argument is too quick. At best what it shows is that an agent could get extra evidence about what their credence is, not that they already have that evidence. But the argument does show something. At least in cases where there is a big range of possible credences, we don’t have to get new evidence to know whether our credence in p is, say 1/2 or 1/3. So I think in realistic examples of Williamsonian cases, Credal Awareness succeeds.

So that leaves Rationality Awareness. I suspect a lot of the time, when we don’t know what our evidence is, we won’t know that we’re responding rationally to our actual evidence. To the extent that rationality just is a matter of responding rationally to evidence, we won’t know that we are rational. I think if we think of rationality this way though, as a matter of people appropriately in tune with the world through our evidence, it shouldn’t be too surprising that we can’t always tell we are rational. Sometimes responding rationally to evidence requires a little luck.