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.
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.