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    Myrvold, Wayne C. 2015. You Can’t Always Get What You Want Some Considerations Regarding Conditional Probabilities. Erkenntnis, Vol. 80, Issue. 3, p. 573.


Full Belief and Probability: Comments on Van Fraassen

  • William Harper (a1) and Alan Hajek (a2)
  • DOI:
  • Published online: 01 April 2010

As van Fraassen pointed out in his opening remarks, Henry Kyburg's lottery paradox has long been known to raise difficulties in attempts to represent full belief as a probability greater than or equal to p, where p is some number less than 1. Recently, Patrick Maher has pointed out that to identify full belief with probability equal to 1 presents similar difficulties. In his paper, van Fraassen investigates ways of representing full belief by personal probability which avoid the difficulties raised by Maher's measure-theoretic version of the lottery paradox. Van Fraassen's more subtle representation dissolves the simple identification of full belief with maximal personal probability. His investigation exploits the richer resources for representing opinion provided by taking conditional, rather than unconditional, personal probability as fundamental. It has interesting implications for equivalent alternative approaches based on non-Archimedean probability, as well as for equivalent approaches in which assumption contexts representing full belief relative to suppositions are taken as fundamental.

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Francis Anscombe , and Robert Aumann 1963A Definition of Subjective Probability.” Annals of Mathematical Statistics, 34: 199205.

William Harper 1975Rational Belief Change, Popper Functions and Counterfactuals.” Synthese, 30: 221–62.

William Harper 1978a “Bayesian Learning Models with Revision of Evidence.” Philosophia, 7, 2: 357–67.

Bas C. van Fraassen 1976Representation of Conditional Probabilities.” Journal of Philosophical Logic, 5: 417–30.

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Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie
  • ISSN: 0012-2173
  • EISSN: 1759-0949
  • URL: /core/journals/dialogue-canadian-philosophical-review-revue-canadienne-de-philosophie
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