Infinitesimal Probabilities

British Journal for the Philosophy of Science 69 (2):509-552 (2016)
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Abstract

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _1_ Introduction _2_ The Limits of Classical Probability Theory _2.1_ Classical probability functions _2.2_ Limitations _2.3_ Infinitesimals to the rescue? _3_ NAP Theory _3.1_ First four axioms of NAP _3.2_ Continuity and conditional probability _3.3_ The final axiom of NAP _3.4_ Infinite sums _3.5_ Definition of NAP functions via infinite sums _3.6_ Relation to numerosity theory _4_ Objections and Replies _4.1_ Cantor and the Archimedean property _4.2_ Ticket missing from an infinite lottery _4.3_ Williamson’s infinite sequence of coin tosses _4.4_ Point sets on a circle _4.5_ Easwaran and Pruss _5_ Dividends _5.1_ Measure and utility _5.2_ Regularity and uniformity _5.3_ Credence and chance _5.4_ Conditional probability _6_ General Considerations _6.1_ Non-uniqueness _6.2_ Invariance Appendix

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Author Profiles

Leon Horsten
Universität Konstanz

Citations of this work

Surreal Decisions.Eddy Keming Chen & Daniel Rubio - 2020 - Philosophy and Phenomenological Research 100 (1):54-74.
Conditional Probabilities.Kenny Easwaran - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 131-198.
Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
Precise Credences.Michael Titelbaum - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 1-55.

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References found in this work

Laws and symmetry.Bas C. Van Fraassen - 1989 - New York: Oxford University Press.
Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
Probability Theory. The Logic of Science.Edwin T. Jaynes - 2002 - Cambridge University Press: Cambridge. Edited by G. Larry Bretthorst.
Laws and Symmetry.Bas C. Van Fraassen - 1989 - Revue Philosophique de la France Et de l'Etranger 182 (3):327-329.

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