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Incommensurability In Mathematics

  • Otávio Bueno
Chapter
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 5)

Abstract

In this paper, as part of an argument for the of revolutions in mathematics, I argue that there in incommensurability in Mathematics. After Devising A Framework Sensitive To Meaning Change And To Changes In The Extension Of Mathematical Predicates, I Consider Two Case Studies That Illustrate Different Ways In Which Incommensurability Emerge In Mathematical Practice. The Most Detailed Case Involves Nonstandard Analysis, And The Existence Of Different Notions Of The Continuum. But I Also Examine How Incommensurability Found Its Way Into Set Theory. I Conclude By Examining Some Consequences That Incommensurability Has To Mathematical Practice.

Keywords

Incommensurability Nonstandard Analysis Set Theory Mathematical Practice 

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Copyright information

© Springer 2007

Authors and Affiliations

  • Otávio Bueno
    • 1
  1. 1.University of South CorolinaUSA

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