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Philosophia Mathematica 2005 13(1):111-113; doi:10.1093/philmat/nki002
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Philosophia Mathematica (III), Vol. 13 No. 1 © Oxford University Press, 2005, all rights reserved

Book Review

Dennis E. Hesseling. Gnomes in the Fog: The Reception of Brouwer's Intuitionism in the 1920s. Basel, Boston, Berlin: Birkhäu-ser Verlag, 2003. Pp. xxiii + 448. ISBN 3-7643-6536-6

Leon Horsten*

* Institute of Philosophy, University of Leuven Kardinaal Mercierplein 2, B-3000 Leuven, Belgium Leon.Horsten@hiw.kuleuven.ac.be

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This book is based on the author's doctoral dissertation. As the subtitle indicates, its main aim is to give a historical and conceptual description of the reception of Brouwer's intuitionism in the 1920s. The first three chapters set the stage. In the first chapter, historical precursors of Brouwer's intuitionism (mainly Kronecker and Poincaré) are discussed. In the second chapter, the genesis and development of Brouwer's foundational view are explained. The third chapter contains an overview of the stances that were taken in the face of the foundational crisis in mathematics in the beginning of the twentieth century. The chapters four and five form the core of the book. In these chapters, a detailed description is . . . [Full Text of this Article]


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