Authors
Alexander R. Pruss
Baylor University
Abstract
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
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DOI 10.1002/tht3.13
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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.

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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.

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