Conditioning using conditional expectations: the Borel-Kolmogorov Paradox.
The Borel-Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes' formula, which loses its mean...
| Publicado en: | Synthese Vol. 194; no. 7; pp. 2595 - 2631 |
|---|---|
| Autores principales: | , , |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Jul2017
|
| 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=124845998&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 124845998 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Jul2017 vid: 194 iid: 7 pid: 237 pub: Springer Nature artinfo: ui: 124845998 10.1007/s11229-016-1070-8 ppf: 2595 ppct: 36 formats: fmt: @attributes: type: P size: 791KB tig: atl: Conditioning using conditional expectations: the Borel-Kolmogorov Paradox. aug: au: Gyenis, Z. Hofer-Szabó, G. Rédei, M. affil: Research Center for the Humanities , Budapest Hungary su: Conditional probability Conditional expectations Intuition Paradox Interpretation (Philosophy) sug: subj: Conditional probability Conditional expectations Intuition Paradox Interpretation (Philosophy) keyword: Borel-Kolmogorov Paradox Conditionalization Interpretation of probability ab: The Borel-Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes' formula, which loses its meaning when the conditioning event has probability zero. We argue in this paper that the theory of conditional expectations is the proper mathematical device to conditionalize and that this theory allows conditionalization with respect to probability zero events. The conditional probabilities on probability zero events in the Borel-Kolmogorov Paradox also can be calculated using conditional expectations. The alleged clash arising from the fact that one obtains different values for the conditional probabilities on probability zero events depending on what conditional expectation one uses to calculate them is resolved by showing that the different conditional probabilities obtained using different conditional expectations cannot be interpreted as calculating in different parametrizations of the conditional probabilities of the same event with respect to the same conditioning conditions. We conclude that there is no clash between the correct intuition about what the conditional probabilities with respect to probability zero events are and the technically proper concept of conditionalization via conditional expectations-the Borel-Kolmogorov Paradox is just a pseudo-paradox. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2017. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2017 holdings: @attributes: islocal: N |
|---|