Abstract

The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how self-locating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments. I show that, contrary to what is commonly accepted, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the ‘thirder’ solution satisfies standard rationality principles, vindicating why it is not vulnerable to diachronic Dutch Book arguments. Moreover, the diachronic Dutch Books against the ‘halfer’ solutions fail to undermine the standard arguments for Conditionalization. The main upshot that emerges from my discussion is that the disagreement between different solutions does not challenge the applicability of Bayesian reasoning to centered settings, nor the commitment to Conditionalization, but is instead an instance of the familiar problem of choosing the priors.

Highlights

  • Adam Elga (2000) introduced to the philosophical literature what has come to be known as the Sleeping Beauty problem: Some researchers are going to put you to sleep

  • As I showed in the previous sections, both the thirder and the halfer solutions can be represented within a Bayesian framework, in a way that is compatible with the principles of Conditionalization and Reflection

  • The Sleeping Beauty problem has generated a great deal of controversy, as all the main attempts to solve it in the literature appear to violate some or other rationality constraint (Titelbaum 2016)

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Summary

Introduction

Adam Elga (2000) introduced to the philosophical literature what has come to be known as the Sleeping Beauty problem: Some researchers are going to put you to sleep. It is often accepted that ‘halfers’ should not bet at the odds that reflect their beliefs in cases like the Sleeping Beauty (Bradley and Leitgeb 2006; Briggs 2009). This puts pressure on the idea that an agent’s credences can generally be interpreted (or operationalised) as the betting odds that the same agent would consider fair, undermining a standard argument for probabilism (de Finetti 1937). ‘it is raining now’, ‘this coin toss landed Tails’) Given this background, this paper makes two contributions. Given that the Bayesian framework is widely regarded as a powerful framework for reasoning under uncertainty, and that there are independent reasons for accepting Conditionalization and Reflection, the results I present shift the burden of proof to those that want to argue for a departure from these principles

The Problem
Further Questions
Prior Perspectives
Solution
A Numerical Answer
Tweaking the Parameters
Matters of Principle
Conditionalization
Reflection
Bets and Odds
Conclusion
Full Text
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