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Proof Theory

History and Philosophical Significance

  • Vincent F. Hendricks
  • Stig Andur Pedersen
  • Klaus Frovin Jørgensen

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction

    1. Hendricks, Pedersen, Jørgensen
      Pages 1-7
  3. Review of Proof Theory

    1. Front Matter
      Pages 9-9
    2. Solomon Feferman
      Pages 11-31
  4. The Background of Hilbert’s Proof Theory

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

    1. Front Matter
      Pages 115-115
    2. Dirk van Dalen
      Pages 117-152
    3. Solomon Feferman
      Pages 179-194
    4. Erhard Scholz
      Pages 195-217
  6. Modern Views and Results from Proof Theory

    1. Front Matter
      Pages 219-219
  7. Back Matter
    Pages 237-257

About this book

Introduction

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.

Keywords

history of mathematics proof proof theory

Editors and affiliations

  • Vincent F. Hendricks
    • 1
  • Stig Andur Pedersen
    • 2
  • Klaus Frovin Jørgensen
    • 2
  1. 1.University of CopenhagenRoskildeDenmark
  2. 2.University of RoskildeRoskildeDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-2796-9
  • Copyright Information Springer Science+Business Media B.V. 2000
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5553-8
  • Online ISBN 978-94-017-2796-9
  • Buy this book on publisher's site