Milan Journal of Mathematics 81 (1):121-151 (2013)

Authors
Leon Horsten
Universität Konstanz
Abstract
We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov’s axiomatization of probability is replaced by a different type of infinite additivity.
Keywords probability  infinitesimals  infinity  Kolmogorov  axioms  Regularity  non-standard models  fair lottery  non-Archimedean fields
Categories (categorize this paper)
Reprint years 2013
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,981
External links

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

Add more references

Citations of this work BETA

Surreal Decisions.Eddy Keming Chen & Daniel Rubio - 2020 - Philosophy and Phenomenological Research 100 (1):54-74.
Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.
Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.

Add more citations

Similar books and articles

Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
On Harold Jeffreys' Axioms.S. Noorbaloochi - 1988 - Philosophy of Science 55 (3):448-452.
Infinite Lotteries, Perfectly Thin Darts and Infinitesimals.Alexander R. Pruss - 2012 - Thought: A Journal of Philosophy 1 (2):81-89.
Countable Additivity and the de Finetti Lottery.Paul Bartha - 2004 - British Journal for the Philosophy of Science 55 (2):301-321.
Probability Logic and Borel's Denumerable Probability.Theodore Hailperin - 2008 - History and Philosophy of Logic 29 (3):307-307.
The Autonomy of Probability Theory (Notes on Kolmogorov, Rényi, and Popper).Hugues Leblanc - 1989 - British Journal for the Philosophy of Science 40 (2):167-181.
Philosophy of Probablilty.Aidan Lyon - 2010 - In Fritz Allhoff (ed.), Philosophies of the Sciences: A Guide. Wiley-Blackwell.
Measurement Without Archimedean Axioms.Louis Narens - 1974 - Philosophy of Science 41 (4):374-393.
What Conditional Probability Could Not Be.Alan Hájek - 2003 - Synthese 137 (3):273--323.

Analytics

Added to PP index
2011-08-30

Total views
155 ( #64,310 of 2,427,508 )

Recent downloads (6 months)
5 ( #147,271 of 2,427,508 )

How can I increase my downloads?

Downloads

My notes