Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s: Science Networks. Historical Studies, cartea 28
Autor Dennis E. Hesselingen Limba Engleză Hardback – 24 oct 2003
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Specificații
ISBN-13: 9783764365363
ISBN-10: 3764365366
Pagini: 476
Ilustrații: XXIII, 448 p.
Dimensiuni: 155 x 235 x 31 mm
Greutate: 0.84 kg
Ediția:2003
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Science Networks. Historical Studies
Locul publicării:Basel, Switzerland
ISBN-10: 3764365366
Pagini: 476
Ilustrații: XXIII, 448 p.
Dimensiuni: 155 x 235 x 31 mm
Greutate: 0.84 kg
Ediția:2003
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Science Networks. Historical Studies
Locul publicării:Basel, Switzerland
Public țintă
ResearchCuprins
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.
Recenzii
"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
—MAA Online
Caracteristici
Reveals a feature of mathematics that is often forgotten or neglected Shows historical roots of one of the important current philosophies of mathematics