But one man's prior is another man's posterior: I can use the belief that a medical test is 90% specific when using it to determine whether a patient has a disease, but I arrived at my beliefs about that medical test through Bayesian processes - either logical reasoning about the science behind the test, or more likely trying the test on a bunch of people and using statistics to estimate a specificity. So it may be mathematically wrong to tell me my 90% prior is false, but the 90% prior from the first question is the same 90% posterior from the second question, and it's totally kosher to say that the 90% posterior from the second question is wrong (and by extension, I'm using the "wrong prior") The whole reflective consistency thing is that you shouldn't have "foundational priors" in the sense that they're not the posterior of anything. Every foundational prior gets checked by how well it accords with other things, and in that sense is sort of a posterior. So I agree with cousin_it that it would be a problem if every Bayesian believed their prior to be correct (as in - they got the correct posterior yesterday to use as their prior today).

Locked in, huh? Then I don't want to be a Bayesian.