Probability Disassembled |
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| Authors: | Norton John D |
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| Institution: | Center for Philosophy of Science, Department of History and Philosophy of Science, University of Pittsburgh, USA |
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| Abstract: | While there is no universal logic of induction, the probabilitycalculus succeeds as a logic of induction in many contexts throughits use of several notions concerning inductive inference. Theyinclude Addition, through which low probabilities representdisbelief as opposed to ignorance; and Bayes property, whichcommits the calculus to a ‘refute and rescale’ dynamicsfor incorporating new evidence. These notions are independentand it is urged that they be employed selectively accordingto needs of the problem at hand. It is shown that neither isadapted to inductive inference concerning some indeterministicsystems. - 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 Universalcomparability
- 3.2.2 Transitivity
- 3.2.3 Monotonicity
- 4 Addition
- 4.1 The property: disbelief versus ignorance
- 4.2Boundaries
- 5 Bayes property
- 5.1 The property
- 5.2 Bayes' theorem
- 5.3Boundaries
- 5.3.1 Dogmatism of the priors
- 5.3.2 Impossibilityof prior ignorance
- 5.3.3 Accommodation of virtues
- 6Real values
- 7 Sufficiency and independence
- 8 Illustrations
- 8.1 All properties retained
- 8.2 Bayes propertyonly retained
- 8.3 Induction without additivity and Bayes property
- 9Conclusion
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