Open Access
2010 On Generalizing Kolmogorov
Richard Dietz
Notre Dame J. Formal Logic 51(3): 323-335 (2010). DOI: 10.1215/00294527-2010-019


In his "From classical to constructive probability," Weatherson offers a generalization of Kolmogorov's axioms of classical probability that is neutral regarding the logic for the object-language. Weatherson's generalized notion of probability can hardly be regarded as adequate, as the example of supervaluationist logic shows. At least, if we model credences as betting rates, the Dutch-Book argument strategy does not support Weatherson's notion of supervaluationist probability, but various alternatives. Depending on whether supervaluationist bets are specified as (a) conditional bets (Cantwell), (b) unconditional bets with graded payoffs (Milne), or (c) unconditional bets with ungraded payoffs(Dietz), supervaluationist probability amounts to (a) conditional probability of truth given a truth-value, (b) the expected truth-value, or (c) the probability of truth, respectively. It is suggested that for supervaluationist logic, the third option is the most attractive one, for (unlike the other options) it preserves respect for single-premise entailment.


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Richard Dietz. "On Generalizing Kolmogorov." Notre Dame J. Formal Logic 51 (3) 323 - 335, 2010.


Published: 2010
First available in Project Euclid: 18 August 2010

zbMATH: 1203.60008
MathSciNet: MR2675685
Digital Object Identifier: 10.1215/00294527-2010-019

Primary: 03B60 , 60A05

Keywords: Probability , supervaluationist logic

Rights: Copyright © 2010 University of Notre Dame

Vol.51 • No. 3 • 2010
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