A Calculus of Regions Respecting Both Measure and Topology.
Say that space is 'gunky' if every part of space has a proper part. Traditional theories of gunk, dating back to the work of Whitehead in the early part of last century, modeled space in the Boolean algebra of regular closed (or regular open) subsets of Euclidean space. More recently a complaint was...
| Publicado en: | Journal of Philosophical Logic Vol. 48; no. 5; pp. 825 - 851 |
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| Autores principales: | , |
| Formato: | Artículo |
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Springer Nature
Oct2019
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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=139501632&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 139501632 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: Oct2019 vid: 48 iid: 5 pid: 237 pub: Springer Nature artinfo: ui: 139501632 10.1007/s10992-018-9496-8 ppf: 825 ppct: 26 formats: fmt: @attributes: type: P size: 570KB tig: atl: A Calculus of Regions Respecting Both Measure and Topology. aug: au: Lando, Tamar Scott, Dana affil: Columbia University, 708 Philosophy Hall, 1150 Amsterdam Ave., Mail Code: 4971, 10027, New York, NY, USA University of California, Berkeley, 1149 Shattuck Avenue, 94707-2609, Berkeley, CA, USA su: Calculus Topology Lebesgue measure Borel subsets Boolean algebra sug: subj: Calculus Topology Lebesgue measure Borel subsets Boolean algebra keyword: Gunk Mereology Mereotopology Point-free space Regions ab: Say that space is 'gunky' if every part of space has a proper part. Traditional theories of gunk, dating back to the work of Whitehead in the early part of last century, modeled space in the Boolean algebra of regular closed (or regular open) subsets of Euclidean space. More recently a complaint was brought against that tradition in Arntzenius (2008) and Russell (2008): Lebesgue measure is not even finitely additive over the algebra, and there is no countably additive measure on the algebra. Arntzenius advocated modeling gunk in measure algebras instead—in particular, in the algebra of Borel subsets of Euclidean space, modulo sets of Lebesgue measure zero. But while this algebra carries a natural, countably additive measure, it has some unattractive topological features. In this paper, we show how to construct a model of gunk that has both nice rudimentary measure-theoretic and topological properties. We then show that in modeling gunk in this way we can distinguish between finite dimensions, and that nothing in lost in terms of our ability to identify points as locations in space. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2019. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2019 holdings: @attributes: islocal: N |
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