Authors
Daniel Hoek
Virginia Tech
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.
Keywords Continuum Hypothesis  Chance  Set Theory  Inductive Reasoning  Countable Additivity  Large Cardinals
Categories (categorize this paper)
DOI 10.1111/phpr.12708
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
Through your library

References found in this work BETA

A Subjectivist’s Guide to Objective Chance.David K. Lewis - 1980 - In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II. Berkeley: University of California Press. pp. 263-293.
Can There Be Vague Objects?Gareth Evans - 1978 - Analysis 38 (4):208.
Theory of Probability.Bruno de Finetti - 1970 - New York: John Wiley.
Subjective Probabilities Should Be Sharp.Adam Elga - 2010 - Philosophers' Imprint 10.
Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.

View all 37 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Is the Dream Solution of the Continuum Hypothesis Attainable?Joel David Hamkins - 2015 - Notre Dame Journal of Formal Logic 56 (1):135-145.
How Woodin Changed His Mind: New Thoughts on the Continuum Hypothesis.Colin J. Rittberg - 2015 - Archive for History of Exact Sciences 69 (2):125-151.
On the Strong Martin Conjecture.Masanori Itai - 1991 - Journal of Symbolic Logic 56 (3):862-875.
Superstable Theories with Few Countable Models.Lee Fong Low & Anand Pillay - 1992 - Archive for Mathematical Logic 31 (6):457-465.
The Metamathematics of Scattered Linear Orderings.P. Clote - 1989 - Archive for Mathematical Logic 29 (1):9-20.
On the Strong Martin Conjecture.Masanori Itai - 1991 - Journal of Symbolic Logic 56 (3):862-875.
Turing Determinacy and the Continuum Hypothesis.Ramez L. Sami - 1989 - Archive for Mathematical Logic 28 (3):149-154.
Global Singularization and the Failure of SCH.Radek Honzik - 2010 - Annals of Pure and Applied Logic 161 (7):895-915.
Chance and Necessity.Daniel Nolan - 2016 - Philosophical Perspectives 30 (1):294-308.

Analytics

Added to PP index
2020-06-13

Total views
615 ( #9,020 of 2,403,030 )

Recent downloads (6 months)
392 ( #895 of 2,403,030 )

How can I increase my downloads?

Downloads

My notes