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date: 22 January 2020

Abstract and Keywords

Kolmogorov's axiomatization of probability is the standard probability axiom system that most people learn in high school or university. And it is widely considered to be undeniably true—in much the same way that arithmetic seems to be undeniably true. However, over the years, various philosophers, mathematicians, statisticians, and scientists have found potential faults with Kolmogorov's axiom system. In this chapter these potential faults are reviewed and discussed. Among them are the problematic countable additivity, as well as finite additivity. The chapter also includes critical examinations of conditional probability, positive real numbers and sets and algebras as deployed by Kolmogorov.

Keywords: probability, axiom system, Kolmogorov, countable additivity finite additivity

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