startTime: 03:35 PM
endTime: 05:00 PM

Geoffrey Hellman and Stewart Shapiro "Authors meet Readers"

Friday, April 5, 2019 3:35PM - 5:00PM

Author Meets Readers

Varieties of Continua: From Regions to Points and Back 

Authors: Geoffrey Hellman Philosophy, University of Minnesota 
Stewart Shapiro Philosophy, The Ohio State University.
Readers: Øystein Linnebo Philosophy, University of Oslo 
Gabriel Uzquiano Philosophy, University of Southern California

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.

This public lecture is free, no registration is required. Contact: Janet McKernan mcps@umn.edu 612-625-6635

155 Nicholson Hall

  • 216 Pillsbury Drive SE
    Minneapolis, MN 55455
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