David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Dissertation, University of Groningen (2011)
This dissertation is a contribution to formal and computational philosophy. In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the introduction of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%.
|Keywords||probability foundations epistemology lottery paradox|
|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
No references found.
Citations of this work BETA
Colin Howson (2013). Finite Additivity, Another Lottery Paradox and Conditionalisation. Synthese:1-24.
Similar books and articles
Sylvia Wenmackers, Danny E. P. Vanpoucke & Igor Douven (2012). Probability of Inconsistencies in Theory Revision. European Physical Journal B 85 (1):44 (15).
Sylvia Wenmackers & Leon Horsten (2013). Fair Infinite Lotteries. Synthese 190 (1):37-61.
Vieri Benci, Leon Horsten & Sylvia Wenmackers (2013). Non-Archimedean Probability. Milan Journal of Mathematics 81 (1):121-151.
Alexander R. Pruss (2012). Infinite Lotteries, Perfectly Thin Darts and Infinitesimals. Thought: A Journal of Philosophy 1 (2):81-89.
Bruce Langtry (1990). Hume, Probability, Lotteries and Miracles. Hume Studies 16 (1):67-74.
Martin Smith (2010). A Generalised Lottery Paradox for Infinite Probability Spaces. British Journal for the Philosophy of Science 61 (4):821-831.
John L. Pollock (1983). Epistemology and Probability. Noûs 17 (1):65-67.
Paolo Rocchi & Leonida Gianfagna, Probabilistic Events and Physical Reality: A Complete Algebra of Probability.
Stephan Hartmann & Jan Sprenger (forthcoming). Bayesian Epistemology. In Duncan Pritchard & Sven Bernecker (eds.), Routledge Companion to Epistemology. Routledge.
Jürgen Humburg (1986). Foundations of a New System of Probability Theory. Topoi 5 (1):39-50.
I. Douven (2012). The Sequential Lottery Paradox. Analysis 72 (1):55-57.
Alan Hájek (2001). Probability, Logic, and Probability Logic. In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell Publishers. 362--384.
Paul Bartha & Christopher Hitchcock (1999). The Shooting-Room Paradox and Conditionalizing on Measurably Challenged Sets. Synthese 118 (3):403-437.
Paul Bartha (2004). Countable Additivity and the de Finetti Lottery. British Journal for the Philosophy of Science 55 (2):301-321.
Patrick Maher (2006). The Concept of Inductive Probability. Erkenntnis 65 (2):185 - 206.
Added to index2011-08-25
Total downloads261 ( #2,616 of 1,696,562 )
Recent downloads (6 months)36 ( #9,077 of 1,696,562 )
How can I increase my downloads?