Valueless Measures on Pointless Spaces.
On our ordinary representations of space, space is composed of indivisible, dimensionless points; extended regions are understood as infinite sets of points. Region-based theories of space reverse this atomistic picture, by taking as primitive several relations on extended regions, and recovering po...
| Publicado en: | Journal of Philosophical Logic Vol. 52; no. 1; pp. 1 - 53 |
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| Formato: | Artículo |
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Springer Nature
Feb2023
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| 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=161549649&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 161549649 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: Feb2023 vid: 52 iid: 1 pid: 237 pub: Springer Nature artinfo: ui: 161549649 10.1007/s10992-022-09652-w ppf: 1 ppct: 52 formats: fmt: @attributes: type: P size: 960KB tig: atl: Valueless Measures on Pointless Spaces. aug: au: Lando, Tamar affil: Department of Philosophy, Columbia University, 708 Philosophy Hall, 1150 Amsterdam Ave., Mail Code: 4971, 10027, New York, NY, USA su: Borel subsets Lebesgue measure Model theory Point set theory Topology sug: subj: Borel subsets Lebesgue measure Model theory Point set theory Topology keyword: Boolean contact algebras Measure algebras Region-based theories of space ab: On our ordinary representations of space, space is composed of indivisible, dimensionless points; extended regions are understood as infinite sets of points. Region-based theories of space reverse this atomistic picture, by taking as primitive several relations on extended regions, and recovering points as higher-order abstractions from regions. Over the years, such theories have focused almost exclusively on the topological and geometric structure of space. We introduce to region-based theories of space a new primitive binary relation ('qualitative probability') that is tied to measure. It expresses that one region is smaller than or equal in size to another. Algebraic models of our theory are separationσ-algebras with qualitative probability: (B , ≪ , ≼) , where B is a Boolean σ-algebra, ≪ is a separation relation on B , and ≼ is a qualitative probability on B . We show that from algebraic models of this kind we can, in an interesting class of cases, recover a compact Hausdorff topology X, together with a countably additive measure μ on a σ-field of Borel subsets of that topology, and that (B , ≪ , ≼) is isomorphic to a 'standard model' arising out of the pair (X, μ). It follows from one of our main results that any closed ball in Euclidean space, ℝ n , together with Lebesgue measure arises in this way from a separation σ-algebra with qualitative probability. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2023. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2023 holdings: @attributes: islocal: N |
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