On Abstraction in Mathematics and Indefiniteness in Quantum Mechanics.
Abstraction turns equivalence into identity, but there are two ways to do it. Given the equivalence relation of parallelness on lines, the #1 way to turn equivalence into identity by abstraction is to consider equivalence classes of parallel lines. The #2 way is to consider the abstract notion of th...
| Publicado en: | Journal of Philosophical Logic Vol. 50; no. 4; pp. 813 - 836 |
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| Formato: | Artículo |
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Springer Nature
Aug2021
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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=151542190&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 151542190 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: Aug2021 vid: 50 iid: 4 pid: 237 pub: Springer Nature artinfo: ui: 151542190 10.1007/s10992-020-09586-1 ppf: 813 ppct: 23 formats: fmt: @attributes: type: P size: 852KB tig: atl: On Abstraction in Mathematics and Indefiniteness in Quantum Mechanics. aug: au: Ellerman, David affil: University of Ljubljana, Ljubljana, Slovenia su: Quantum mechanics Quantum superposition Probability theory Mathematics Mathematical models sug: subj: Quantum mechanics Quantum superposition Probability theory Mathematics Mathematical models keyword: Abstraction Indefiniteness in quantum mechanics Superposition ab: Abstraction turns equivalence into identity, but there are two ways to do it. Given the equivalence relation of parallelness on lines, the #1 way to turn equivalence into identity by abstraction is to consider equivalence classes of parallel lines. The #2 way is to consider the abstract notion of the direction of parallel lines. This paper developments simple mathematical models of both types of abstraction and shows, for instance, how finite probability theory can be interpreted using #2 abstracts as "superposition events" in addition to the ordinary events. The goal is to use the second notion of abstraction to shed some light on the notion of an indefinite superposition in quantum mechanics. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2021. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
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