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Probability disassembled

Norton, JD (2007) Probability disassembled. British Journal for the Philosophy of Science, 58 (2). 141 - 171. ISSN 0007-0882

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Abstract

While there is no universal logic of induction, the probability calculus succeeds as a logic of induction in many contexts through its use of several notions concerning inductive inference. They include Addition, through which low probabilities represent disbelief as opposed to ignorance; and Bayes property, which commits the calculus to a 'refute and rescale' dynamics for incorporating new evidence. These notions are independent and it is urged that they be employed selectively according to needs of the problem at hand. It is shown that neither is adapted to inductive inference concerning some indeterministic systems. 1 Introduction 2 Failure of demonstrations of universality 2.1 Working backwards 2.2 The surface logic 3 Framework 3.1 The properties 3.2 Boundaries 3.2.1 Universal comparability 3.2.2 Transitivity 3.2.3 Monotonicity 4 Addition 4.1 The property: disbelief versus ignorance 4.2 Boundaries 5 Bayes property 5.1 The property 5.2 Bayes' theorem 5.3 Boundaries 5.3.1 Dogmatism of the priors 5.3.2 Impossibility of prior ignorance 5.3.3 Accommodation of virtues 6 Real values 7 Sufficiency and independence 8 Illustrations 8.1 All properties retained 8.2 Bayes property only retained 8.3 Induction without additivity and Bayes property 9 Conclusion. © The Author (2007). Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved.


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Details

Item Type: Article
Status: Published
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Norton, JDjdnorton@pitt.eduJDNORTON
Centers: University Centers > Center for Philosophy of Science
Date: 1 June 2007
Date Type: Publication
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Journal or Publication Title: British Journal for the Philosophy of Science
Volume: 58
Number: 2
Page Range: 141 - 171
DOI or Unique Handle: 10.1093/bjps/axm009
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > History and Philosophy of Science
Refereed: Yes
ISSN: 0007-0882
Article Type: Review
Date Deposited: 12 Jul 2012 14:00
Last Modified: 02 Feb 2019 15:56
URI: http://d-scholarship.pitt.edu/id/eprint/12557

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