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Proof Theory

History and Philosophical Significance

  • Book
  • © 2000

Overview

Editors:
  1. Vincent F. Hendricks

    1. University of Copenhagen, Roskilde, Denmark

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  2. Stig Andur Pedersen

    1. University of Roskilde, Roskilde, Denmark

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  3. Klaus Frovin Jørgensen

    1. University of Roskilde, Roskilde, Denmark

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Part of the book series: Synthese Library (SYLI, volume 292)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    1. Introduction

      • Hendricks, Pedersen, Jørgensen
      Pages 1-7

  3. Review of Proof Theory

    1. Front Matter

      Pages 9-9
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    2. Hightlights in Proof Theory

      • Solomon Feferman
      Pages 11-31

  4. The Background of Hilbert’s Proof Theory

    1. Front Matter

      Pages 33-33
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    2. The Empiricist Roots of Hilbert’s Axiomatic Approach

      • Leo Corry
      Pages 35-54

    3. The Calm Before the Storm: Hilbert’s Early Views on Foundations

      • David Rowe
      Pages 55-93

    4. Toward Finitist Proof Theory

      • Wilfried Sieg
      Pages 95-114

  5. Brouwer and Weyl on Proof Theory and Philosophy of Mathematics

    1. Front Matter

      Pages 115-115
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    2. The Development of Brouwer’s Intuitionism

      • Dirk van Dalen
      Pages 117-152

    3. Did Brouwer’s Intuitionistic Analysis Satisfy Its Own Epistemological Standards?

      • Moritz Epple
      Pages 153-178

    4. The Significance of Weyl’s Das Kontinuum

      • Solomon Feferman
      Pages 179-194

    5. Herman Weyl on the Concept of Continuum

      • Erhard Scholz
      Pages 195-217

  6. Modern Views and Results from Proof Theory

    1. Front Matter

      Pages 219-219
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    2. Relationships between Constructive, Predicative and Classical Systems of Analysis

      • Solomon Feferman
      Pages 221-236

  7. Back Matter

    Pages 237-257
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Keywords

About this book

hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math­ ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se­ cure foundation by formalizing all of mathematics and subsequently prove consistency of these formal systems by finitistic means. Hence proof theory was developed as a formal tool through which this goal should be fulfilled. It is well known that Hilbert's Programme in its original form was unfeasible mainly due to Gtldel's incompleteness theorems. Additionally it proved impossible to formalize all of mathematics and impossible to even prove the consistency of relatively simple formalized fragments of mathematics by finitistic methods. In spite of these problems, Gentzen showed that by extending Hilbert's proof theory it would be possible to prove the consistency of interesting formal systems, perhaps not by finitis­ tic methods but still by methods of minimal strength. This generalization of Hilbert's original programme has fueled modern proof theory which is a rich part of mathematical logic with many significant implications for the philosophy of mathematics.

Editors and Affiliations

  • University of Copenhagen, Roskilde, Denmark

    Vincent F. Hendricks

  • University of Roskilde, Roskilde, Denmark

    Stig Andur Pedersen, Klaus Frovin Jørgensen

Bibliographic Information

  • Book Title: Proof Theory

  • Book Subtitle: History and Philosophical Significance

  • Editors: Vincent F. Hendricks, Stig Andur Pedersen, Klaus Frovin Jørgensen

  • Series Title: Synthese Library

  • DOI: https://doi.org/10.1007/978-94-017-2796-9

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2000

  • Hardcover ISBN: 978-0-7923-6544-0Published: 30 September 2000

  • Softcover ISBN: 978-90-481-5553-8Published: 05 December 2010

  • eBook ISBN: 978-94-017-2796-9Published: 09 March 2013

  • Series ISSN: 0166-6991

  • Series E-ISSN: 2542-8292

  • Edition Number: 1

  • Number of Pages: XII, 257

  • Topics: Logic, Mathematical Logic and Foundations, History of Mathematical Sciences, Philosophy of Science

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