Notre Dame Journal of Formal Logic

On Generalizing Kolmogorov

Richard Dietz

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Abstract

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.

Article information

Source
Notre Dame J. Formal Logic Volume 51, Number 3 (2010), 323-335.

Dates
First available in Project Euclid: 18 August 2010

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1282137985

Digital Object Identifier
doi:10.1215/00294527-2010-019

Mathematical Reviews number (MathSciNet)
MR2675685

Zentralblatt MATH identifier
05773614

Subjects
Primary: 60A05: Axioms; other general questions 03B60: Other nonclassical logic

Keywords
probability supervaluationist logic

Citation

Dietz, Richard. On Generalizing Kolmogorov. Notre Dame J. Formal Logic 51 (2010), no. 3, 323--335. doi:10.1215/00294527-2010-019. http://projecteuclid.org/euclid.ndjfl/1282137985.


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References

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