Authors
Matthew Parker
London School of Economics
Abstract
In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable symmetry principles. Moreover, the examples here are immune to the objections against Williamson’s infinite coin flips.
Keywords Regularity  Euclidean set size  Probability  Infinitesimal probabilities  Non-Archimedean probabilities  Jaynes  Objective Bayesianism
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References found in this work BETA

Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
A Subjectivist’s Guide to Objective Chance.David K. Lewis - 1980 - In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II. Berkeley: University of California Press. pp. 263-293.
Truth and Probability.Frank Ramsey - 1926 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 52-94.
Two Dogmas of Empiricism.W. V. Quine - 1951 - In Robert B. Talisse & Scott F. Aikin (eds.), The Pragmatism Reader: From Peirce Through the Present. Princeton University Press. pp. 202-220.

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Citations of this work BETA

Symmetry Arguments Against Regular Probability: A Reply to Recent Objections.Matthew Parker - 2018 - European Journal for Philosophy of Science 9 (1):8.
Symmetry Arguments Against Regular Probability: A Reply to Recent Objections.Matthew Parker - 2019 - European Journal for Philosophy of Science 9 (1):1-21.

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