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Quitting CertaintiesA Bayesian Framework Modeling Degrees of Belief$
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Michael G. Titelbaum

Print publication date: 2012

Print ISBN-13: 9780199658305

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199658305.001.0001

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The Proper Expansion Principle

The Proper Expansion Principle

Chapter:
(p.170) (p.171) 8 The Proper Expansion Principle
Source:
Quitting Certainties
Author(s):

Michael G. Titelbaum

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199658305.003.0008

This chapter examines the difficulties self-locating degrees of belief cause for traditional Bayesian modeling frameworks. It argues that these problems are caused not by Bayesianism’s view of the contents to which degrees of belief are assigned, but instead by the way Conditionalization (the traditional Bayesian updating norm) interacts with context-sensitive claims. Solving these problems requires us first to understand the interactions between formal models of the same story based on different modeling languages. A Proper Expansion Principle (PEP) is proposed that governs such interactions. Combining PEP with Generalized Conditionalization (an updating rule defended in previous chapters) yields the Certainty-Loss Framework (CLF), a formal framework that correctly models rational requirements in stories involving context-sensitivity. The version of PEP presented in this chapter improves on earlier versions proposed by the author, which were susceptible to a counterexample invented by Sarah Moss.

Keywords:   self-locating belief, context-sensitivity, Generalized Conditionalization, conditionalization, Proper Expansion Principle, modeling, Sarah Moss, Bayesianism, Certainty-Loss Framework

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