Year 2018, Volume 8, Issue 2, Pages 455 - 469 2018-12-30

Popper's Axiomatic Probability System and the Value-Assignment Problem

Mehmet Hilmi Demir [1]

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In the standard theory of probability, developed by Kolmogorov, the concept of conditional probability is defined with what is known as the ratio formula: the probability of A given B is the ratio between the probability of A and B and the probability of B, i.e. P(A|B)= (P(AB))/(P(B)). Clearly, this ratio is not defined when the probability of the condition, P(B), is 0. According to Popper, this problem, which is known as the zero-denominator problem, shows a serious conceptual shortcoming of the standard Kolmogorovian theory of probability. In order to overcome this shortcoming, Popper developed an alternative axiomatic theory of probability where conditional probability is taken as primitive. It should be noted that this axiomatic probability theory is different than and independent from Popper’s philosophy of probability which is based on the propensity approach. Popper claims that his axiomatic theory is a better fit for the use of probability in the philosophy of science and statistics. Based on this claim, it is often stated that Popper’s theory is conceptually superior to Kolmogorov’s theory. The ultimate aim of this paper is to evaluate this claim by analyzing Popper’s axiomatic theory within the context of the zero-denominator problem. 

Conditional probability, Popper, Kolmogorov, Hájek, Zero denominator problem
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Primary Language en
Subjects Philosophy
Journal Section Articles

Author: Mehmet Hilmi Demir
Institution: Middle East Technical University
Country: Turkey

APA Demir, M . (2018). Popper's Axiomatic Probability System and the Value-Assignment Problem. Beytulhikme An International Journal of Philosophy, 8 (2), 455-469. Retrieved from