David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 89 (2):257 - 283 (2008)
In this paper a theory of finitistic and frequentistic approximations — in short: f-approximations — of probability measures P over a countably infinite outcome space N is developed. The family of subsets of N for which f-approximations converge to a frequency limit forms a pre-Dynkin system $D \subseteq \wp (N)$ . The limiting probability measure over D can always be extended to a probability measure over $\wp (N)$ , but this measure is not always σ-additive. We conclude that probability measures can be regarded as idealizations of limiting frequencies if and only if σ-additivity is not assumed as a necessary axiom for probabilities. We prove that σ-additive probability measures can be characterized in terms of so-called canonical and in terms of so-called full f-approximations. We also show that every non-σ-additive probability measure is f-approximable, though neither canonically nor fully f-approximable. Finally, we transfer our results to probability measures on open or closed formulas of first-order languages
|Keywords||Philosophy Computational Linguistics Mathematical Logic and Foundations Logic|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
John Earman (1992). Bayes or Bust? Bradford.
Kevin Kelly (1996). The Logic of Reliable Inquiry. Oxford University Press, USA.
Henry Ely Kyburg (1961). Probability and the Logic of Rational Belief. Middletown, Conn.,Wesleyan University Press.
Citations of this work BETA
Sylvia Wenmackers & Leon Horsten (2013). Fair Infinite Lotteries. Synthese 190 (1):37-61.
Frederik Herzberg (2010). The Consistency of Probabilistic Regresses. A Reply to Jeanne Peijnenburg and David Atkinson. Studia Logica 94 (3):331-345.
Leendert Huisman (2015). Reflecting on Finite Additivity. Synthese 192 (6):1785-1797.
Similar books and articles
Mohamed A. Amer (1985). Extension of Relatively |Sigma-Additive Probabilities on Boolean Algebras of Logic. Journal of Symbolic Logic 50 (3):589 - 596.
J. Williamson (1999). Countable Additivity and Subjective Probability. British Journal for the Philosophy of Science 50 (3):401-416.
Teddy Seidenfeld, Remarks on the Theory of Conditional Probability: Some Issues of Finite Versus Countable Additivity.
Cory F. Juhl (1996). Objectively Reliable Subjective Probabilities. Synthese 109 (3):293 - 309.
John D. Norton (2007). Disbelief as the Dual of Belief. International Studies in the Philosophy of Science 21 (3):231 – 252.
Sven Ove Hansson (2009). Measuring Uncertainty. Studia Logica 93 (1):21 - 40.
Vieri Benci, Leon Horsten & Sylvia Wenmackers (2013). Non-Archimedean Probability. Milan Journal of Mathematics 81 (1):121-151.
John C. Bigelow (1979). Quantum Probability in Logical Space. Philosophy of Science 46 (2):223-243.
Chunlai Zhou (2010). Probability Logic of Finitely Additive Beliefs. Journal of Logic, Language and Information 19 (3):247-282.
Added to index2009-01-28
Total downloads440 ( #2,862 of 1,907,606 )
Recent downloads (6 months)108 ( #2,435 of 1,907,606 )
How can I increase my downloads?