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Varieties of Continua – From Regions to Points and Back | Oxford Scholarship Online
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Varieties of Continua: From Regions to Points and Back

Geoffrey Hellman and Stewart Shapiro

Abstract

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 (stemming from the work of Bolzano, Cauchy, Weierstrass, Dedekind, Cantor, et al.). The second is the mid-to-late twentieth-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Ab ... More

Keywords: continuity, infinity, punctiform, point, region, Aristotle, geometry, analysis

Bibliographic Information

Print publication date: 2018 Print ISBN-13: 9780198712749
Published to Oxford Scholarship Online: March 2018 DOI:10.1093/oso/9780198712749.001.0001

Authors

Affiliations are at time of print publication.

Geoffrey Hellman, author
University of Minnesota

Stewart Shapiro, author
Ohio State University