Chance and the Continuum Hypothesis

dc.contributor.authorHoek, Danielen
dc.date.accessioned2022-01-16T17:40:38Zen
dc.date.available2022-01-16T17:40:38Zen
dc.date.issued2021-12-06en
dc.date.updated2022-01-16T17:40:35Zen
dc.description.abstractThis 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.en
dc.description.versionAccepted versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.orcidHoek, Daniel [0000-0002-5331-2409]en
dc.identifier.urihttp://hdl.handle.net/10919/107679en
dc.language.isoenen
dc.relation.urihttp://arxiv.org/abs/2112.12858v1en
dc.relation.urihttps://doi.org/10.1111/phpr.12708en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectmath.HOen
dc.subjectmath.LOen
dc.titleChance and the Continuum Hypothesisen
dc.title.serialPhilosophy and Phenomenological Researchen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Liberal Arts and Human Sciencesen
pubs.organisational-group/Virginia Tech/Liberal Arts and Human Sciences/Philosophyen
pubs.organisational-group/Virginia Tech/Liberal Arts and Human Sciences/CLAHS T&R Facultyen
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