Smooth Infinitesimals in the Metaphysical Foundation of Spacetime Theories.
I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry (SIG) based on certain algebraic objects (i.e., rings), which regiments a mode of reasoning heuristically used by geometricists and physicists (e.g., circle is composed of infinitely many straight lines). I a...
| Publicado en: | Journal of Philosophical Logic Vol. 51; no. 4; pp. 857 - 878 |
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| Formato: | Artículo |
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Springer Nature
Aug2022
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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=157956646&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 157956646 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: Aug2022 vid: 51 iid: 4 pid: 237 pub: Springer Nature artinfo: ui: 157956646 10.1007/s10992-022-09653-9 ppf: 857 ppct: 21 formats: fmt: @attributes: type: P size: 407KB tig: atl: Smooth Infinitesimals in the Metaphysical Foundation of Spacetime Theories. aug: au: Chen, Lu affil: Philosophy Department, Koc University, Istanbul, Turkey su: Spacetime Infinitesimal geometry Vector fields Whole & parts (Philosophy) Physicists Algebra sug: subj: Spacetime Infinitesimal geometry Vector fields Whole & parts (Philosophy) Physicists Algebra keyword: Continuum Einstein algebras Nonclassical mereology Smooth infinitesimal analysis Smooth infinitesimal geometry Tangent space Vectorial quantity ab: I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry (SIG) based on certain algebraic objects (i.e., rings), which regiments a mode of reasoning heuristically used by geometricists and physicists (e.g., circle is composed of infinitely many straight lines). I argue that SIG has the following utilities. (1) It provides a simple metaphysics of vector fields and tangent space that are otherwise perplexing. A tangent space can be considered an infinitesimal region of space. (2) It generalizes a standard implementation of spacetime algebraicism (according to which physical fields exist fundamentally without an underlying manifold) called Einstein algebras. (3) It solves the long-standing problem of interpreting smooth infinitesimal analysis (SIA) realistically, an alternative foundation of spacetime theories to real analysis (Lawvere Cahiers de Topologie et Géométrie Différentielle Catégoriques, 21(4), 277–392, 1980). SIA is formulated in intuitionistic logic and is thought to have no classical reformulations (Hellman Journal of Philosophical Logic, 35, 621–651, 2006). Against this, I argue that SIG is (part of) such a reformulation. But SIG has an unorthodox mereology, in which the principle of supplementation fails. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2022. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2022 holdings: @attributes: islocal: N |
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