Thanks cipergoth, for raising this fundamental issue. I'll try to defend the "no belief" approach, since I still consider it possibly correct. However, it should be noted that other options include credence intervals, for example "somewhere between almost-certain and certain, inclusive".
On the first argument - you have to make a decision, but it needn't literally be a calculated decision.
On the second, I would suggest a model of thought which has more continuity. In between "no belief" and a precise numerical probability could lie various qualitative assessments of the evidence for and against. On this model, the precise probabilities that a speaker might avow for certain select bets are good-enough approximations to a belief-state that may not quite fully live up to that precision. The exact numerical probabilities are used because expected utility calculations are a convenient approach to certain decisions. The jump from qualitative to numerical probabilities is made when the perceived advantages of expected utility calculations justify it - and perhaps the jump is more verbal than real.
Teddy Seidenfeld has a critique of maximum-entropy priors which, to my admittedly ill-trained eye, looks like a serious problem. I would love to believe that every probability question has an objective answer. But I don't, at least not yet.
Sorry if this seems incomplete - thought I'd fire this off as a discussion post now and hope to return to it with a more well-rounded post later.
Less Wrongers are used to thinking of uncertainty as best represented as a probability - or perhaps as a log odds ratio, stretching from minus infinity to infinity. But when I argue with people about for example cryonics, it appears most people consider that some possibilities simply don't appear on this scale at all: that we should not sign up for cryonics because no belief about its chances of working can be justified. Rejecting this category seems to me one of the key foundational ideas of this community, but as far as I know the only article specifically discussing it is "I don't know", which doesn't make a devastatingly strong case. What other writing discusses this idea?
I think there are two key arguments against this. First, you have to make a decision anyway, and the "no belief" uncertainty doesn't help with that. Second, "no belief" is treated as disconnected from the probability line; so at some point evidence causes a discontinuous jump from "no belief" to some level of confidence. This discontinuity seems very unnatural. How can evidence add up to a discontinuous jump - what happened to all the evidence before the jump?