Ten Reasons to Care About the Sleeping Beauty Problem

2013 ◽  
Vol 8 (11) ◽  
pp. 1003-1017 ◽  
Author(s):  
Michael G. Titelbaum
Keyword(s):  
Sleeping Beauty ◽  
Sleeping Beauty Problem

Generalized Conditionalization and the Sleeping Beauty Problem

Erkenntnis ◽  
2011 ◽  
Vol 78 (2) ◽  
pp. 333-351 ◽  
Author(s):  
Terry Horgan ◽  
Anna Mahtani
Keyword(s):  
Sleeping Beauty ◽  
Sleeping Beauty Problem

Direct Inference, Reichenbach's Principle, and the Sleeping Beauty Problem

Episteme ◽  
2019 ◽  
pp. 1-14
Author(s):  
Terry Horgan
Keyword(s):  
Binary Relation ◽  
Single Case ◽  
Sleeping Beauty ◽  
General Information ◽  
Statistical Nature ◽  
Sleeping Beauty Problem ◽  
Direct Inference

Abstract A group of philosophers led by the late John Pollock has applied a method of reasoning about probability, known as direct inference and governed by a constraint known as Reichenbach's principle, to argue in support of ‘thirdism’ concerning the Sleeping Beauty Problem. A subsequent debate has ensued about whether their argument constitutes a legitimate application of direct inference. Here I defend the argument against two extant objections charging illegitimacy. One objection can be overcome via a natural and plausible definition, given here, of the binary relation ‘logically stronger than’ between two properties that can obtain even when the respective properties differ from one another in ‘arity’; given this definition, the Pollock group's argument conforms to Reichenbach's principle. Another objection prompts a certain refinement of Reichenbach's principle that is independently well-motivated. My defense of the Pollock group's argument has epistemological import beyond the Sleeping Beauty problem, because it both widens and sharpens the applicability of direct inference as a method for inferring single-case epistemic probabilities on the basis of general information of a probabilistic or statistical nature.

scholarly journals Sleeping Beauty on Monty Hall

Philosophies ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 15
Author(s):  
Michel Janssen ◽  
Sergio Pernice
Keyword(s):  
Simple Model ◽  
Philosophy Of Science ◽  
Sleeping Beauty ◽  
Simple Solution ◽  
Degrees Of Belief ◽  
Sleeping Beauty Problem ◽  
Game Show ◽  
Bayes’S Theorem ◽  
Monty Hall ◽  
Monty Hall Problem

Inspired by the Monty Hall Problem and a popular simple solution to it, we present a number of game-show puzzles that are analogous to the notorious Sleeping Beauty Problem (and variations on it), but much easier to solve. We replace the awakenings of Sleeping Beauty by contestants on a game show, like Monty Hall’s, and increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to make it easier to see what the solution to the problem is. We show that these game-show proxies for the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-and-true strategy for addressing problems in philosophy of science, i.e., develop a simple model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, much more so than the Monty Hall Problem, challenges the intuitions about probabilities of many when they first encounter it, the application of this strategy to this conundrum, we believe, is pedagogically useful.

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