The way a rational agent changes her belief in certain
propositions/hypotheses in the light of new evidence lies at the heart of
Bayesian inference. The basic natural assumption, as summarized in van
Fraassen's Reflection Principle ([1984]), would be that in the absence of new
evidence the belief should not change. Yet, there are examples that are claimed
to violate this assumption. The apparent paradox presented by such examples, if
not settled, would demonstrate the inconsistency and/or incompleteness of the
Bayesian approach and without eliminating this inconsistency, the approach
cannot be regarded as scientific.
The Sleeping Beauty Problem is just such an example. The existing attempts to
solve the problem fall into three categories. The first two share the view that
new evidence is absent, but differ about the conclusion of whether Sleeping
Beauty should change her belief or not, and why. The third category is
characterized by the view that, after all, new evidence (although hidden from
the initial view) is involved.
My solution is radically different and does not fall in either of these
categories. I deflate the paradox by arguing that the two different degrees of
belief presented in the Sleeping Beauty Problem are in fact beliefs in two
different propositions, i.e. there is no need to explain the (un)change of
belief.Comment: 7 pages, MSWord, to appear in The British Journal for the Philosophy
of Scienc
