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One Hundred Years of Intuitionism (1907-2007)

The Cerisy Conference

  • Book
  • © 2008

Overview

Editors:
  1. Mark Atten

    1. IHPST, CNRS/Paris I/ENS, Paris, France

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  2. Pascal Boldini

    1. CAMS-EHESS, Université Paris-Sorbonne Maison de la Recherche, Paris, France

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  3. Michel Bourdeau

    1. IHPST, CNRS/Paris I/ENS, Paris, France

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  4. Gerhard Heinzmann

    1. Archives H. Poincaré, Nancy-Université/CNRS, Nancy CX, France

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  • Large variety of facets studied: biographical, contextual, philosophical, logical, and mathematical
  • Significant progress on problems central to current foundational studies
  • Brings together 21 contributions of today's leading authors on intuitionism
  • Rich introduction to those new to research in the field
  • Includes supplementary material: sn.pub/extras

Part of the book series: Publications des Archives Henri Poincaré Publications of the Henri Poincaré Archives (PAHP)

Part of the book sub series: Science autour de / around 1900 (PAHPSCIENCE)

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Table of contents (22 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Brouwer and Brouwerian intuitionism

    1. Front Matter

      Pages 1-1
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    2. Another look at Brouwer’s dissertation

      • Dirk van Dalen
      Pages 3-20

    3. Brouwerian infinity

      • Carl Posy
      Pages 21-36

    4. The new intuitionism

      • Charles McCarty
      Pages 37-49

    5. Truth and experience of truth

      • Jacques Dubucs
      Pages 50-59

    6. The proper explanation of intuitionistic logic: on Brouwer’s demonstration of the Bar Theorem

      • Göran Sundholm, Mark van Atten
      Pages 60-77

    7. The intersection of intuitionism (Brouwer) and phenomenology (Husserl)

      • Richard Tieszen
      Pages 78-95

    8. Brouwer on ‘hypotheses’ and the middle Wittgenstein

      • Mathieu Marion
      Pages 96-114

    9. Brouwer’s notion of intuition and theory of knowledge by presence

      • Mohammad Ardeshir
      Pages 115-130

    10. Buddhist models of the mind and the common core thesis on mysticism

      • Hank Barendregt
      Pages 131-145

  4. Mathematical perspectives

    1. Front Matter

      Pages 241-241
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    2. The Hilbert-Brouwer controversy resolved?

      • Per Martin-Löf
      Pages 243-256

    3. Proof theory and Martin-Löf Type Theory

      • Anton Setzer
      Pages 257-279
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Keywords

About this book

With logicism and formalism, intuitionism is one of the main foundations for mathematics proposed in the twentieth century; and since the seventies, notably its views on logic have become important also outside foundational studies, with the development of theoretical computer science.

The aim of the book is threefold: to review and complete the historical account of intuitionism; to present recent philosophical work on intuitionism; and to give examples of new technical advances and applications of intuitionism. This volume brings together 21 contributions by today's leading authors on these topics, and surveys the philosophical, logical and mathematical implications of the approach initiated in 1907 in L.E.J. Brouwer's dissertation.

Editors and Affiliations

  • IHPST, CNRS/Paris I/ENS, Paris, France

    Mark Atten, Michel Bourdeau

  • CAMS-EHESS, Université Paris-Sorbonne Maison de la Recherche, Paris, France

    Pascal Boldini

  • Archives H. Poincaré, Nancy-Université/CNRS, Nancy CX, France

    Gerhard Heinzmann

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