From Kolmogorov, to Popper, to Renyi: There's No Escaping Humphreys' Paradox (When Generalized)

Abstract

Humphreys� Paradox (Humphreys 1985) can be solved if propensity theorists (i) adopt R�nyi�s 1955 probability axiom system as the correct axiom system for propensities and (ii) maintain that there are no backwards propensities in the world. A similar move can be used to solve Milne�s Problem (Milne 1985)�another common objection to the propensity interpretation. That�s the good news. However, Humphreys� Paradox and Milne�s Problem are just two special cases of a much more general problem, and this problem causes trouble even for propensity theorists who accept (i) and (ii). That�s the bad news. Show more