Two historical episodes form the background to the research presented here: 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 entirely of points to the now standard, entirely punctiform fra...

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Bibliographic Details

Main Authors:	Hellman, Geoffrey (Author), Shapiro, Stewart 1951- (Author)
Format:	Electronic eBook
Language:	English
Published:	Oxford Oxford University Press 2018
Edition:	First edition
Subjects:	Continuity Mathematik Kontinuum
Online Access:	Volltext
Summary:	Two historical episodes form the background to the research presented here: 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 entirely of points to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts. The second is the mid-to-late 20th-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Abraham Robinson, and the more radical smooth infinitesimal analysis based on intuitionistic logic. One goal of this work is to develop a systematic comparison of these. A second goal is to develop thoroughgoing regions-based theories of classical continua that are mathematically equivalent to the currently standard, punctiform accounts of modern texts
Item Description:	This edition previously issued in print: 2018
ISBN:	9780191781087
DOI:	10.1093/oso/9780198712749.001.0001