Let me mention one other objection to the indifference
principle Adam defends in his Dr Evil paper.
Imagine that Dakota is duplicated infinitely many times, so she has a countable
infinity of epistemic duplicates. Let F₀ be the property of
being Dakota, and for all integers n, F_n the property
of being the n^th duplicate. Then according to INDIFFERENCE, Dakota’s
credence that she satisfies F_i should be identical for all
non-negative integers i. Since there are infinitely many such properties,
and they are exclusive, this means that either (a) her degree of belief that
she satisfies a particular F_i must be 0, or (b) that degree
of belief must be some kind of infinitesimal. If (a) then we have a violation
of countable additivity, for Dakota’s credence that she is either F₀
or F₁ or … is 1. So INDIFFERENCE either implies violations of
countable additivity, or it implies the existence of certain distinctive kinds
of infinitesimal valued degrees of belief. Neither of these are disastrous
options, but neither is perfectly happy either.