Imprecise probabilities is a theory born of our limitations as reasoning agents, and of limitations in our evidence base. If only we had better evidence, a single probability function would do. But since our evidence is weak, we must use a set. In a way, the same is true of precise probabilism. If only we knew the truth, we could represent belief with a truth-valuation function, or just a set of sentences that are fully believed. But since there are truths we don’t know, we must use a probability to represent our intermediate confidence. And indeed, the same problem arises for the imprecise probabilist. Is it reasonable to assume that we know what set of probabilities best represents the evidence? Perhaps we should have a set of sets of probabilities… Similar problems arise for theories of vagueness (Sorensen 2012). We objected to precise values for degrees of belief, so why be content with sets-valued beliefs with precise boundaries? This is the problem of “higher-order vagueness” recast as a problem for imprecise probabilism. Why is sets of probabilities the right level to stop the regress at? Why not sets of sets? Why not second-order probabilities? Why not single probability functions? Williamson (2014) makes this point, and argues that a single precise probability is the correct level at which to get off the “uncertainty escalator”. Williamson advocates the betting interpretation of belief, and his argument here presupposes that interpretation. But the point is still worth addressing: for a particular interpretation of what belief is, what sort of level of uncertainty is appropriate. For the functionalist interpretation suggested above, this is something of a pragmatic choice. The further we allow this regress to continue, the harder it is to deal with these belief-representing objects. So let’s not go further than we need.