Chance and the Continuum Hypothesis

Philosophy and Phenomenological Research 103 (3):639-60 (2021)
  Copy   BIBTEX

Abstract

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.

Similar books and articles

The metamathematics of scattered linear orderings.P. Clote - 1989 - Archive for Mathematical Logic 29 (1):9-20.
Defending the Indispensability Argument: Atoms, Infinity and the Continuum.Eduardo Castro - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):41-61.
Pointwise definable models of set theory.Joel David Hamkins, David Linetsky & Jonas Reitz - 2013 - Journal of Symbolic Logic 78 (1):139-156.
Superstable theories with few countable models.Lee Fong Low & Anand Pillay - 1992 - Archive for Mathematical Logic 31 (6):457-465.
On the strong Martin conjecture.Masanori Itai - 1991 - Journal of Symbolic Logic 56 (3):862-875.

Analytics

Added to PP
2020-06-13

Downloads
1,807 (#5,555)

6 months
282 (#8,259)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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.

View all 39 references / Add more references