In some unfortunate situations, rationality doesn't allow you to settle on a stable opinion. These are cases where becoming more confident that things will go one way gives you evidence that they'll go the other way; and vice versa. In these cases, any belief you adopt undermines itself. I suggest that in such scenarios you should adopt imprecise probabilities. This connects to accounts for the liar paradox, in particular a supervaluational version of Kripke's account of truth.