Journal Article

Probability Disassembled

John D. Norton

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 58, issue 2, pages 141-171
Published in print June 2007 | ISSN: 0007-0882
Published online May 2007 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axm009
Probability Disassembled

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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

Journal Article.  11787 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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