Chance and the Continuum Hypothesis
| dc.contributor.author | Hoek, Daniel | en |
| dc.date.accessioned | 2022-01-16T17:40:38Z | en |
| dc.date.available | 2022-01-16T17:40:38Z | en |
| dc.date.issued | 2021-12-06 | en |
| dc.date.updated | 2022-01-16T17:40:35Z | en |
| dc.description.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. | en |
| dc.description.version | Accepted version | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.orcid | Hoek, Daniel [0000-0002-5331-2409] | en |
| dc.identifier.uri | http://hdl.handle.net/10919/107679 | en |
| dc.language.iso | en | en |
| dc.relation.uri | http://arxiv.org/abs/2112.12858v1 | en |
| dc.relation.uri | https://doi.org/10.1111/phpr.12708 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | math.HO | en |
| dc.subject | math.LO | en |
| dc.title | Chance and the Continuum Hypothesis | en |
| dc.title.serial | Philosophy and Phenomenological Research | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |
| pubs.organisational-group | /Virginia Tech | en |
| pubs.organisational-group | /Virginia Tech/All T&R Faculty | en |
| pubs.organisational-group | /Virginia Tech/Liberal Arts and Human Sciences | en |
| pubs.organisational-group | /Virginia Tech/Liberal Arts and Human Sciences/Philosophy | en |
| pubs.organisational-group | /Virginia Tech/Liberal Arts and Human Sciences/CLAHS T&R Faculty | en |
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