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The British Journal for the Philosophy of Science Advance Access originally published online on May 23, 2007
The British Journal for the Philosophy of Science 2007 58(2):141-171; doi:10.1093/bjps/axm009
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Copyright © The Author 2007. Published by Oxford University Press on behalf of British Society for the Philosophy of Science.

Probability Disassembled

John D. Norton

Center for Philosophy of Science, Department of History and Philosophy of Science, University of Pittsburgh, USA

jdnorton+{at}pitt.edu


  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


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