The end of Sleeping Beauty's nightmare

TL;DR

This paper addresses the Sleeping Beauty Problem by proposing a novel solution that deflates the paradox, arguing that the conflicting beliefs are about different propositions, thus avoiding the need to explain belief change.

Contribution

It introduces a new perspective by showing the two degrees of belief are about different propositions, resolving the paradox without assuming belief update.

Findings

The paradox is deflated by distinguishing beliefs about different propositions.

The approach avoids the need for belief updating in the paradox.

It challenges existing categories of solutions to the Sleeping Beauty Problem.

Abstract

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.