Chapter

Strict Coherence, Sigma Coherence, and the Metaphysics of Quantity

Brian Skyrms

in From Zeno to Arbitrage

Published in print November 2012 | ISBN: 9780199652808
Published online January 2013 | e-ISBN: 9780191745829 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199652808.003.0005
Strict Coherence, Sigma Coherence, and the Metaphysics of Quantity

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Probability is a quantity. Do all events have a probability? Are there real possibilities that have zero probability? Do we have countable additivity? The standard theory of probability, due to Kolmogorov, takes the mathematics of probability to be the standard mathematics of normalized measure and adopts the answers that this theory delivers. But leading figures in modern probability theory, including Kolmogorov himself, de Finetti, and Savage, have argued in one way or another that this theory is philosophically wrong. Sigma-coherence (immunity from a Dutch book with a countable number of bets) and strict coherence initially appear to pull in different directions, but the turn out to be compatible in the setting of measure algebras.

Keywords: strict coherence; sigma additivity; infinitesimal; measure algebra

Chapter.  6449 words. 

Subjects: Philosophy of Science

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