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Author:   Dennis E. Hesseling
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2003 ed.
Volume:   28
Dimensions:   Width: 15.50cm , Height: 2.60cm , Length: 23.50cm
Weight:   1.860kg
ISBN:  

9783764365363

ISBN 10:   3764365366
Pages:   448
Publication Date:   24 October 2003
Audience:   General/trade ,  General
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

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.

Reviews

L.E.J. Brouwer is best known to many mathematicians for his seminal contributions to topology. He is also the founder of mathematical intuitionism, and a key player in the debate on foundations of mathematics that raged for a brief decade in the 1920s, and then subsided. Gnomes in the Fog tells the story of that important and influential episode in the history of mathematics, in fascinating and delicious detail... [A]nyone with an interest in mathematics and its history and philosophy, should enjoy this book. Mathematicians (especially logicians) may find some surprises in the first chapter, on Brouwer's predecessors; philosophers and science study scholars should especially appreciate the final chapter on the cultural context of the debate... One of the many treasures to be discovered in reading this book is the rich collection of original quotes in the many languages in which the debate took place, along with the author's translations. --MAA Online

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