Sleeping Beauty on Monty Hall

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.

Uncomputable but complete physics theory of the universe

It is often assumed that the complete physics theory of the universe is computable - in sense that it can provide meaningful theoretical predictions for every phenomenon of the universe. Against this view, it is argued that once quantum mechanics is understood as encompassing a novel concept of probability, thereby resolving the measurement problem in straightforward ways, the interpretation speaks for uncomputability of the complete physics theory. The reasons why a new theory of probability is needed are explored, along the lines of the principle of indifference and the sleeping beauty problem.

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

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.

Self-Locating Credences

An agent's self-locating credences capture her opinions about who she is, where she is, and what time it is. Most authors agree that self-locating credences cannot be rationally updated simply by applying traditional Bayesian conditionalization. After explaining why this is, I catalog alternative updating schemes that have been proposed for self-locating credence. I separate those schemes into three broad approaches: ‘shifting schemes’, ‘stable base schemes’, and ‘demonstrative schemes’. Each approach solves particular problems but has its particular blindspots. I then suggest that the Sleeping Beauty Problem has generated so much controversy in the literature because it falls into the blindspots of all three types of updating schemes.