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Being Rational and Being Right$
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Juan Comesaña

Print publication date: 2020

Print ISBN-13: 9780198847717

Published to Oxford Scholarship Online: April 2020

DOI: 10.1093/oso/9780198847717.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 13 June 2021

Probability and Decision Theory

Probability and Decision Theory

Chapter:
(p.6) 2 Probability and Decision Theory
Source:
(p.iii) Being Rational and Being Right
Author(s):

Juan Comesaña

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198847717.003.0002

This chapter introduces the mathematics of probability and decision theory. The probability calculus is introduced in both a set-theoretic and a propositional context. Probability is also related to measure theory, and stochastic truth-tables are presented. Problems with conditional probability are examined. Two interpretations of the probability calculus are introduced: physical and normative probabilities. The problem of logical omniscience for normative probabilities is discussed. Dutch Book arguments and accuracy-based arguments for Probabilism (the claim that our credences must satisfy the probability axioms) are examined and rejected. Different interpretations of the “idealization” reply to the problem of logical omniscience are considered, and one of them is tentatively endorsed. The expected utility maximization conception of decision theory is introduced, and representation arguments are considered (and rejected) as another reply to the problem of logical omniscience.

Keywords:   probability, decision theory, logical omniscience, idealization, Dutch Book argument

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