Gnomes in the Fog The Reception of Brouwer’s Intuitionism in the 1920s

Gnomes in the Fog The Reception of Brouwer’s Intuitionism in the 1920s / by Dennis E. Hesseling.

The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet. The found...

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Bibliographic Details
Main Author: Hesseling, Dennis E. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2003.
Edition:1st ed. 2003.
Series:Science Networks. Historical Studies, 28
Springer eBook Collection.
Subjects:
Mathematics.
History.
Mathematical logic.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1 Kronecker, the semi-intuitionists, Poincaré
  • 1.1 Introduction
  • 1.2 Kronecker
  • 1.3 The French semi-intuitionists
  • 1.4 Poincaré
  • 1.5 Conclusion
  • 2 The genesis of Brouwer’s intuitionism
  • 2.1 Introduction
  • 2.2 The early years
  • 2.3 The first act of intuitionism
  • 2.4 Topology
  • 2.5 Intuitionism and formalism
  • 2.6 The second act of intuitionism
  • 2.7 The Brouwer lectures
  • 2.8 The Mathematische Annalen and afterwards
  • 2.9 Brouwer’s personality
  • 2.10 Conclusion
  • 3 Overview of the foundational debate
  • 3.1 Introduction
  • 3.2 Quantitative inquiry
  • 3.3 Qualitative inquiry
  • 3.4 Conclusion
  • 4 Reactions: existence and constructivity
  • 4.1 Introduction
  • 4.2 The beginning of the debate
  • 4.3 The debate widened
  • 4.4 Later reactions
  • 4.5 Conclusion
  • 5 Reactions: logic and the excluded middle
  • 5.1 Introduction
  • 5.2 The beginning of the debate
  • 5.3 The debate widened
  • 5.4 Later reactions
  • 5.5 Conclusion
  • 6 The foundational crisis in its context
  • 6.1 Introduction
  • 6.2 Metaphors
  • 6.3 Philosophy
  • 6.4 Physics
  • 6.5 Art
  • 6.6 Politics
  • 6.7 Moderne and Gegenmoderne
  • 6.8 Conclusion
  • Conclusion
  • A Chronology of the debate
  • B Public reactions to Brouwer’s intuitionism
  • C Logical notations
  • Dankwoord/ Acknowledgements.

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