Abstract

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.

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