Bertrand's Paradox is a Paradox of Infinity.
Since its formulation in the nineteenth century, Bertrand's paradox has played a prominent role in discussions of probability theory and has received a great deal of attention from philosophers, mathematicians, and physicists alike. This is because the paradox is often interpreted as refuting the Pr...
| Publicado en: | Synthese Vol. 206; no. 2; pp. 1 - 33 |
|---|---|
| Autor principal: | |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Aug2025
|
| 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=186677862&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 186677862 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Aug2025 vid: 206 iid: 2 pid: 237 pub: Springer Nature artinfo: ui: 186677862 10.1007/s11229-025-05140-1 ppf: 1 ppct: 32 formats: fmt: – @attributes: type: T – @attributes: type: P size: 4.1MB tig: atl: Bertrand's Paradox is a Paradox of Infinity. aug: au: Ryan, Patrick J. affil: https://ror.org/0190ak572 Department of Philosophy, New York University, 10003, New York, NY, USA su: Probability theory Nineteenth century Paradox Philosophers Intuition sug: subj: Probability theory Nineteenth century Paradox Philosophers Intuition keyword: Cantor's principle Geometrical paradoxes Infinity Paradoxes of infinity Probability ab: Since its formulation in the nineteenth century, Bertrand's paradox has played a prominent role in discussions of probability theory and has received a great deal of attention from philosophers, mathematicians, and physicists alike. This is because the paradox is often interpreted as refuting the Principle of Indifference, a central pillar of classical probability theory. In this paper, I articulate a novel interpretation of Bertrand's paradox according to which it is ultimately a paradox of infinity produced by a conflict between our intuitions and techniques for measuring infinite sets and the properties we wish to preserve when doing so. I proceed by first analyzing Bertrand's original formulation of the paradox and show that one can make sense of this discussion entirely in terms how we deal with the infinite sets in question. I then discuss two possible approaches for dealing with this construal and argue that the paradox can be avoided by jettisoning our Cantorian intuitions for measuring infinite sets. Next, I analyze recent mathematical frameworks developed to resolve the paradox and argue that disagreement between these accounts indicates that a "meta-level" Bertrand's paradox is lurking in the wings. This recurrence of the paradox leads us into deep questions about the possible indeterminacy latent in all attempts to measure infinite sets. Finally, I take stock of what we have learned from my analysis, delineate possible approaches for dealing with the meta-level paradox, and suggest directions for future research. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2025. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2025 holdings: @attributes: islocal: N |
|---|