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A NEW ARGUMENT FOR KOLOMOGOROV CONDITIONALIZATION

Part of: Foundations of probability theory

Published online by Cambridge University Press:  21 July 2020

MICHAEL NIELSEN
MICHAEL NIELSEN*
Affiliation:
DEPARTMENT OF PHILOSOPHY THE UNIVERSITY OF SYDNEYNSW2006, AUSTRALIA E-mail: michael.nielsen@sydney.edu.au
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Abstract

This paper contributes to a recent research program that extends arguments supporting elementary conditionalization to arguments supporting conditionalization with general, measure-theoretic conditional probabilities. I begin by suggesting an amendment to the framework that Rescorla (2018) has used to characterize regular conditional probabilities in terms of avoiding Dutch book. If we wish to model learning scenarios in which an agent gains complete membership knowledge about some subcollection of the events of interest to her, then we should focus on updating policies that are what I shall call proper. I go on to characterize regular conditional probabilities in proper learning scenarios using what van Fraassen (1999) calls The General Reflection Principle.

Keywords

conditionalizationKolmogorovregular conditional probabilityreflection principle

MSC classification

Primary: 60A05: Axioms; other general questions
Secondary: 60A10: Probabilistic measure theory
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 4 , December 2021 , pp. 930 - 945
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Copyright
© Association for Symbolic Logic, 2020

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