David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic, Language and Information 19 (3):247-282 (2010)
Probability logics have been an active topic of investigation of beliefs in type spaces in game theoretical economics. Beliefs are expressed as subjective probability measures. Savage’s postulates in decision theory imply that subjective probability measures are not necessarily countably additive but finitely additive. In this paper, we formulate a probability logic Σ + that is strongly complete with respect to this class of type spaces with finitely additive probability measures, i.e. a set of formulas is consistent in Σ + iff it is satisfied in a finitely additive type space. Although we can characterize Σ + -theories satisfiable in the class as maximally consistent sets of formulas, we prove that any canonical model of maximally consistent sets is not universal in the class of type spaces with finitely additive measures, and, moreover, it is not a type space. At the end of this paper, we show that even a minimal use of probability indices causes the failure of compactness in probability logics.
|Keywords||Probabilistic beliefs Type spaces Reasoning about probabilities Modal 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
Leonard J. Savage (1954). The Foundations of Statistics. Wiley Publications in Statistics.
J. Williamson (1999). Countable Additivity and Subjective Probability. British Journal for the Philosophy of Science 50 (3):401-416.
Colin Howson (2008). De Finetti, Countable Additivity, Consistency and Coherence. British Journal for the Philosophy of Science 59 (1):1-23.
Citations of this work BETA
James Andow (2015). How Distinctive Is Philosophers’ Intuition Talk? Metaphilosophy 46 (4-5):515-538.
Similar books and articles
Daniele Mundici (1995). Averaging the Truth-Value in Łukasiewicz Logic. Studia Logica 55 (1):113 - 127.
Douglas E. Ensley (1996). Automorphism-Invariant Measures on ℵ0-Categorical Structures Without the Independence Property. Journal of Symbolic Logic 61 (2):640 - 652.
John D. Norton (2007). Disbelief as the Dual of Belief. International Studies in the Philosophy of Science 21 (3):231 – 252.
Piers Rawling (1997). Perspectives on a Pair of Envelopes. Theory and Decision 43 (3):253-277.
Teddy Seidenfeld & Mark J. Schervish (1983). A Conflict Between Finite Additivity and Avoiding Dutch Book. Philosophy of Science 50 (3):398-412.
Teddy Seidenfeld, Remarks on the Theory of Conditional Probability: Some Issues of Finite Versus Countable Additivity.
Mohamed A. Amer (1985). Extension of Relatively |Sigma-Additive Probabilities on Boolean Algebras of Logic. Journal of Symbolic Logic 50 (3):589 - 596.
G. Schurz & H. Leitgeb (2008). Finitistic and Frequentistic Approximation of Probability Measures with or Without Σ -Additivity. Studia Logica 89 (2):257 - 283.
Added to index2009-10-10
Total downloads49 ( #97,687 of 1,932,544 )
Recent downloads (6 months)5 ( #197,566 of 1,932,544 )
How can I increase my downloads?