Quote:
Originally Posted by bbbeard
Are you saying it's a theorem that p(H  E1 & E2) = p(H  ~E1 & E2) = p(H  E2)?

No. I'm saying that the conjunction of
p(H  E1) > p(H),
and
p(H  E1 & E2) = p(H  ~E1 & E2) = p(H  E2)
might very well happen in this particular case.
Quote:
I frankly don't even understand what you mean by the "probability that H is true given E1".

I'm using "the probability that H is true given E1" to mean "the amount of credence that you ought to have in H if E1 is your only evidence."
Quote:
In what universe could the "probability" of H depend on the prior opinions of experts?

Again, probability is the proper amount of credence. So, if the prior opinions of experts is the best evidence you have on the matter, your credence should depend on those opinions.