Chance and the Continuum Hypothesis

Philosophy and Phenomenological Research 103 (3):639-60 (2021)
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This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum.

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Daniel Hoek
Virginia Tech

References found in this work

The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
The Foundations of Statistics.Leonard J. Savage - 1956 - Philosophy of Science 23 (2):166-166.
The Foundations of Statistics.Leonard J. Savage - 1954 - Synthese 11 (1):86-89.
Evidential Symmetry and Mushy Credence.Roger White - 2009 - Oxford Studies in Epistemology 3:161-186.

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