Hoppa till sidans huvudinnehåll

1 509 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

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.

Produktinformation

  • Utgivningsdatum2018-02-15
  • Mått164 x 240 x 19 mm
  • Vikt492 g
  • FormatInbunden
  • SpråkEngelska
  • Antal sidor220
  • FörlagOUP OXFORD
  • ISBN9780198712749

Tillhör följande kategorier

Hoppa över listan

Mer från samma författare

Mathematics without Numbers

Geoffrey Hellman, University of Minnesota) Hellman, Geoffrey (Professor of Philosophy, Professor of Philosophy

Häftad

1 059 kr

The History of Continua

Stewart Shapiro, Stewart Shapiro, Geoffrey Hellman, Ohio State University) Shapiro, Stewart (O'Donnell Professor of Philosophy, University of Minnesota) Hellman, Geoffrey (Professor of Philosophy

Inbunden

2 949 kr

Mathematical Structuralism

Geoffrey Hellman, Stewart Shapiro, Geoffrey (University of Minnesota) Hellman, Stewart (Ohio State University) Shapiro

Häftad

319 kr

Hoppa över listan

Du kanske också är intresserad av

Varieties of Logic

Stewart Shapiro, Stewart (Ohio State University) Shapiro, SHAPIRO, Shapiro

Inbunden

1 489 kr

Classical First-Order Logic

Stewart Shapiro, Teresa Kouri Kissel, Stewart (Ohio State University) Shapiro, Virginia) Kissel, Teresa Kouri (Old Dominion University

Häftad

289 kr

Varieties of Logic

Stewart Shapiro, Stewart (Ohio State University) Shapiro, Shapiro, SHAPIRO

Häftad

559 kr

The History of Continua

Stewart Shapiro, Stewart Shapiro, Geoffrey Hellman, Ohio State University) Shapiro, Stewart (O'Donnell Professor of Philosophy, University of Minnesota) Hellman, Geoffrey (Professor of Philosophy

Inbunden

2 949 kr

Mathematical Structuralism

Geoffrey Hellman, Stewart Shapiro, Geoffrey (University of Minnesota) Hellman, Stewart (Ohio State University) Shapiro

Häftad

319 kr

Mathematics without Numbers

Geoffrey Hellman, University of Minnesota) Hellman, Geoffrey (Professor of Philosophy, Professor of Philosophy

Häftad

1 059 kr