Another question arising in this matter is how to treat evidence of extraordinary things. Should one require ‘extraordinary evidence for extraordinary claims’? I somehow feel that this notion is misguided—it discriminates evidence prior to observation. That is not the right time to start discriminating. At most we should ascribe a prior probability of zero and then do some Bayesian updating to get a posterior.
As ParagonProtege noted below, if your prior is 0, then your posterior is also zero no matter how compelling the evidence you observe. As I understand it, the statement “extraordinary claims require extraordinary evidence” is simply pointing out that because extraordinary claims have low priors, you need a relatively large amount of evidence to shift them up. That is, it is not trying to tell you how to treat evidence, just describing the situation you find yourself in when updating extraordinary beliefs.
As ParagonProtege noted below, if your prior is 0, then your posterior is also zero no matter how compelling the evidence you observe. As I understand it, the statement “extraordinary claims require extraordinary evidence” is simply pointing out that because extraordinary claims have low priors, you need a relatively large amount of evidence to shift them up. That is, it is not trying to tell you how to treat evidence, just describing the situation you find yourself in when updating extraordinary beliefs.