If we're going to talk about how and why we should formulate priors, rather than what Bayes' rule says, this is what we're interested in.
But that's not what I'm talking about. I was specifically responding to your claim that:
"prior probability", by definition, means that we throw out all previous evidence.
So far as I can tell, that's not part of the accepted definition. For example, Jaynes' work on prior probabilities explicitly invokes prior information:
in two problems where we have the same prior information, we should assign the same prior probabilities.
I don't mean to come off as a dick for nit-picking about definitions. But rigorous mathematical definitions are really important, especially if you are claiming to argue something is true by definition - and you were.
Yes, I was wrong. I was explaining why I got so focused on the blank-slate version of the prior.
Recently I've been struck with a belief in Aliens being present on this Earth. It happened after I watched this documenary (and subsequently several others). My feeling of belief is not particular interesting in itself - I could be lunatic or otherwise psychological dysfunctional. What I'm interested in knowing is to what extend other people, who consider themselves rationalists, feel belief in the existence of aliens on this earth, after watching this documentary. Is anyone willing to try and watch it and then report back?
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. Hmm, if no one has seen a black swan and some bayesian thinking person then sees a black swan a) in the distance or b) up front, what will his a posterior probability of the existence of black swans then be?