David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 156 (3):491-512 (2007)
Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is new is that it is shown that probabilistic consistency and consequence can be defined in a way formally analogous to the way these notions are defined in deductive (propositional) logic. The result is a free-standing logic which does not pretend to be a theory of rationality and is therefore immune to, among other charges, that of “logical omniscience”.
|Keywords||Probability Utility Odds Logic Consistency|
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Ernest Adams (1965). The Logic of Conditionals. Inquiry 8 (1-4):166 – 197.
Richard Bradley (1998). A Representation Theorem for a Decision Theory with Conditionals. Synthese 116 (2):187-229.
Bruno de Finetti (1972). Probability, Induction, and Statistics. New York: John Wiley.
Bruno de Finetti (1970). Theory of Probability. New York: John Wiley.
John Earman (1992). Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. MIT Press.
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