Chance and the Continuum Hypothesis.
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 pro...
| Publicado en: | Philosophy & Phenomenological Research Vol. 103; no. 3; pp. 639 - 661 |
|---|---|
| Formato: | Artículo |
| Publicado: |
Wiley-Blackwell
Nov2021
|
| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=154834420&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 154834420 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00318205 PPO jtl: Philosophy & Phenomenological Research issn: 00318205 maglogo: Y pubinfo: dt: Nov2021 vid: 103 iid: 3 pid: 480 pub: Wiley-Blackwell artinfo: ui: 154834420 10.1111/phpr.12708 ppf: 639 ppct: 22 formats: fmt: @attributes: type: P size: 1.3MB tig: atl: Chance and the Continuum Hypothesis. aug: su: Continuum hypothesis Set theory Generalized continuum hypothesis Probabilistic number theory Axioms sug: subj: Continuum hypothesis Set theory Generalized continuum hypothesis Probabilistic number theory Axioms ab: 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Philosophy & Phenomenological Research is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Philosophy & Phenomenological Research holder: Wiley-Blackwell dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
|---|