The idea is rejecting classical foundationalism and accepting the idea that people come into a topic from various perspectives. We are called upon to adjust the beliefs we have rather than start from scratch. So to begin, any prior is OK, but in the light of evidence, if the case is really strong, everyone can move from where they are to a consensus.
As I understand it, everyone's prior probabilities (even people who believe weird things) are "properly basic" and we revise from there.
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But how did everyone come to adopt their perspectives? Presumably, through evidence of some kind. But the weight of that evidence can, too, be judged by Bayes' theorem. Regressing back, we will find ourselves in a state in which we have no evidence either for or against a belief and are therefore ready to use Bayes' theorem for the first time on our first piece of evidence. At this point our priors should all be equal, but to what? To 50%?
Or is that which differentiates our priors background knowledge K which will differ from person to person? But, again, that knowledge can be broken up into pieces of evidence and those evaluated with the help of Bayes' theorem.
I agree that in practice people will have different priors, and that's an ultimate given of a sort. But in principle can't those priors be reduced or deconstructed in the manner described?
I'm more interested in developing a practical model for evaluating arguments. Either prior probabilities really are subjective, or else I don't know how to figure out "correct" prior probabilities. Either way, this is a way of analyzing how one goes about changing one's mind in the light of evidence.
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