Sleeping Beauty, Countable Additivity, and Rational Dilemmas
Bibliographic Data
| ID | 10693708 |
|---|---|
| Authors | Jacob Ross (corresponding author) |
| Year | 2010 |
| Volume | 119 |
| Issue | 4 |
| Pages | 411-447 |
| Publication date | 2010-10-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | The Philosophical Review (JOURNAL) |
| Journal identifiers | ISSN: 0031-8108 • E-ISSN: 1558-1470 |
| Publisher | Duke University Press (PUBLISHER • US) |
| DOI | 10.1215/00318108-2010-010 |
| OpenAlex | W1982654186 |
| Language | EN |
| Citations received | 9 |
| References cited | 34 |
This essay argues that there is a conflict between the principle of Countable Additivity and standard views of how we should update centered or de se beliefs. The latter views, this essay argues, entail a general principle, which the essay calls the Generalized Thirder Principle, that conflicts with the principle of Countable Additivity. The essay then argues that the most plausible response to the conflict between these principles is to maintain that they are both valid and that, when an agent cannot satisfy them both, he or she is faced with a rational dilemma. The essay is divided into five sections. In section 1, it generalizes the one-half and one-third solutions to the Sleeping Beauty problem. In section 2, it argues that while the Generalized Halfer Principle is compatible with Countable Additivity (CA), the Generalized Thirder Principle (GTP) is not. In section 3, it argues that thirders are committed to the GTP since it follows from the premises that underlie each of the main arguments for the one-third solution. In section 4, it discusses the relevance of Dutch book arguments to the conflict between CA and the GTP. And the essay argues that both synchronic and diachronic Dutch book arguments give greater support to CA than to the GTP. In the final section, the essay considers the possible responses to the conflict between CA and the GTP and argues that the most plausible response is to acknowledge the possibility of rational dilemmas
Beauty · Countable set · Dilemma · Epistemology · GTP · Physics · Pure mathematics · Rationality · Section (typography) · Sociology · Computer Science · Epistemology, Ethics, and Metaphysics · Free Will and Agency · Mathematics · Philosophy · Philosophy and Theoretical Science
Centering the Principal Principle
Conceptual limitations, puzzlement, and epistemic dilemmas
Belief and rational indeterminacy
Finite additivity, another lottery paradox and conditionalisation
Dilemmic Epistemology
Rationality is Not Coherence
Sleeping Beauty
Finite Frequentism in a Big World
Ten Reasons to Care About the Sleeping Beauty Problem
Pragmatics and Empiricism
Statistical Reasoning with Imprecise Probabilities
The Logic of Reliable Inquiry
The Foundations of Causal Decision Theory
Self-locating belief and the Sleeping Beauty problem
Belief and the Will
Synchronic Bayesian updating and the Sleeping Beauty problem
Diachronic Dutch Books and Sleeping Beauty
Beauty and the Bets
What Conditional Probability Could Not Be
The Relevance of Self-Locating Beliefs
Clever Bookies and Coherent Beliefs
Defeating Dr. Evil with Self‐Locating Belief
Should We Respond to Evil with Indifference
De Finetti, Countable Additivity, Consistency and Coherence
Countable Additivity and the de Finetti Lottery
Countable Additivity and Subjective Probability
| Unique citing works | 9 |
|---|---|
| Citations per year | 0,69 |
| Citation span | 2013 - 2023 (11) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 9 |