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.
Product Identifiers
Publisher
Oxford University Press
ISBN-13
9780198712749
eBay Product ID (ePID)
22046413843
Product Key Features
Author
Stewart Shapiro, Geoffrey Hellman
Publication Name
Varieties of Continua: from Regions to Points and Back
Format
Hardcover
Language
English
Subject
Mathematics
Publication Year
2018
Type
Textbook
Number of Pages
220 Pages
Dimensions
Item Height
240 mm
Item Width
164 mm
Item Weight
492 g
Additional Product Features
Country/Region of Manufacture
United Kingdom
Title_Author
Stewart Shapiro, Geoffrey Hellman
Topic
Popular Philosophy
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