Alexander R. Pruss
Baylor University
One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on the books: a measure that assigns the same infinitesimal probability to each number between zero and one. I will show that such a measure, while mathematically interesting, is pathological for use in confirmation theory, for the same reason that a measure that assigns an infinitesimal probability to each possible outcome in a countably infinite lottery is pathological. The pathology is that one can force someone to assign a probability within an infinitesimal of one to an unlikely event
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1002/tht3.13
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 50,308
Through your library

References found in this work BETA

The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
The Foundations of Statistics.Leonard J. Savage - 1959 - Synthese 11 (1):86-89.

View all 7 references / Add more references

Citations of this work BETA

Infinitesimal Probabilities.Sylvia Wenmackers - 2016 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.
You’Ve Come a Long Way, Bayesians.Jonathan Weisberg - 2015 - Journal of Philosophical Logic 44 (6):817-834.
Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia9 Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
The Normative Status of Logic.Florian Steinberger - 2017 - Stanford Enyclopedia of Philosophy.

View all 14 citations / Add more citations

Similar books and articles

Non-Archimedean Probability.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2013 - Milan Journal of Mathematics 81 (1):121-151.
Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
Lagrange Lecture: Methodology of Numerical Computations with Infinities and Infinitesimals.Yaroslav Sergeyev - 2010 - Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.
Throwing Darts, Time, and the Infinite.Jeremy Gwiazda - 2013 - Erkenntnis 78 (5):971-975.
Quantum Probability in Logical Space.John C. Bigelow - 1979 - Philosophy of Science 46 (2):223-243.
Objective Probabilities in Number Theory.J. Ellenberg & E. Sober - 2011 - Philosophia Mathematica 19 (3):308-322.
When Can Statistical Theories Be Causally Closed?Balazs Gyenis & Miklos Redei - 2002 - Foundations of Physics 34 (9):1285-1303.
Perspectives on a Pair of Envelopes.Piers Rawling - 1997 - Theory and Decision 43 (3):253-277.


Added to PP index

Total views
97 ( #93,798 of 2,325,999 )

Recent downloads (6 months)
2 ( #445,586 of 2,325,999 )

How can I increase my downloads?


My notes