Varieties of continua

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Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate the underlying metaphysical issues concerning the nature of space or space-time.



Varieties of Continua explores the development of the idea of the continuous. Hellman and Shapiro begin with two historical episodes. The first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view, that a true continuum cannot be composed of points, to the now standard, point-based frameworks for analysis and geometry found in modern mainstream mathematics (stemming from the work of Bolzano, Cauchy, Weierstrass, Dedekind, Cantor, et al.). The second is the mid-tolate-twentieth century revival of pre-limit methods in analysis and geometry using infinitesimals including non-standard analysis (due to Abraham Robinson), and the more radical smooth infinitesimal analysis that uses intuitionistic logic. Hellman and Shapiro present a systematic comparison of these and related alternatives (including constructivist and predicative conceptions), weighing various trade-offs, helping articulate a modern pluralist perspective, and articulate a modern pluralist perspective on continuity. The main creative work of the book is the development of rigorous regions-based theories of classical continua, including Euclidean and non-Euclidean geometries, that are mathematically equivalent (inter-reducible) to the currently standard, point-based accounts in mainstream mathematics.

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Taal: en

Bindwijze: Hardcover

Oorspronkelijke releasedatum: 15 februari 2018

Aantal pagina's: 224

Illustraties: Nee

Hoofdauteur: Geoffrey Hellman

Tweede Auteur: Stewart Shapiro

Hoofduitgeverij: Oxford University Press

Extra groot lettertype: Nee

Product breedte: 164 mm

Product hoogte: 19 mm

Product lengte: 240 mm

Studieboek: Ja

Verpakking breedte: 164 mm

Verpakking hoogte: 19 mm

Verpakking lengte: 240 mm

Verpakkingsgewicht: 492 g

EAN: 9780198712749

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