“THE WHOLE IS GREATER THAN THE PART." MEREOLOGY IN EUCLID'S ELEMENTS.
The present article provides a mereological analysis of Euclid's planar geometry as presented in the first two books of his Elements. As a standard of comparison, a brief survey of the basic concepts of planar geometry formulated in a set-theoretic framework is given in Section 2. Section 3.2, then,...
| Publicado en: | Logic & Logical Philosophy Vol. 25; no. 3; pp. 371 - 410 |
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| Formato: | Artículo |
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Logic & Logical Philosophy
2016
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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=117618785&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 117618785 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 14253305 DS9 jtl: Logic & Logical Philosophy issn: 14253305 maglogo: N pubinfo: dt: 2016 vid: 25 iid: 3 pid: 42904 pub: Logic & Logical Philosophy artinfo: ui: 117618785 10.12775/LLP.2016.011 ppf: 371 ppct: 39 formats: fmt: @attributes: type: P size: 3MB tig: atl: “THE WHOLE IS GREATER THAN THE PART." MEREOLOGY IN EUCLID'S ELEMENTS. aug: au: Robering, Klaus affil: Department of Communciation and Design, University of Southern Denmark, Kolding, Denmark su: Whole & parts (Philosophy) Convex geometry Euclidean algorithm Mathematical continuum Measure theory sug: subj: Whole & parts (Philosophy) Convex geometry Euclidean algorithm Mathematical continuum Measure theory keyword: atomistic mereology continuum convex geometry Euclidean plane measure theory points polygons ab: The present article provides a mereological analysis of Euclid's planar geometry as presented in the first two books of his Elements. As a standard of comparison, a brief survey of the basic concepts of planar geometry formulated in a set-theoretic framework is given in Section 2. Section 3.2, then, develops the theories of incidence and order (of points on a line) using a blend of mereology and convex geometry. Section 3.3 explains Euclid's “megethology", i.e., his theory of magnitudes. In Euclid's system of geometry, megethology takes over the role played by the theory of congruence in modern accounts of geometry. Mereology and megethology are connected by Euclid's Axiom 5: “The whole is greater than the part." Section 4 compares Euclid's theory of polygonal area, based on his “Whole-Greater-Than-Part" principle, to the account provided by Hilbert in his Grundlagen der Geometrie. An hypothesis is set forth why modern treatments of geometry abandon Euclid's Axiom 5. Finally, in Section 5, the adequacy of atomistic mereology as a framework for a formal reconstruction of Euclid's system of geometry is discussed. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Logic & Logical Philosophy is the property of Logic & Logical Philosophy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Logic & Logical Philosophy holder: Logic & Logical Philosophy dt: @attributes: year: 2016 holdings: @attributes: islocal: N |
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