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Saved from the Cellar

Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics

  • Jan von Plato

Table of contents

  1. Front Matter
    Pages i-x
  2. Jan von Plato
    Pages 97-303
  3. Back Matter
    Pages 305-315

About this book

Introduction

Gerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today. Another noteworthy achievement is his resolution of the embarrassing situation created by Gödel's incompleteness results, especially the second one about the unprovability of consistency of elementary arithmetic. After these successes, Gentzen dedicated the rest of his short life to the main problem of Hilbert's proof theory, the question of the consistency of analysis. He was arrested in the summer of 1945 with other professors of the German University of Prague and died soon afterward of starvation in a prison cell. Attempts at locating his lost manuscripts failed at the time, but several decades later, two slim folders of shorthand notes were found. In this volume, Jan von Plato gives an overview of Gentzen's life and scientific achievements, based on detailed archival and systematic studies, and essential for placing the translations of shorthand manuscripts that follow in the right setting. The materials in this book are singular in the way they show the birth and development of Gentzen's central ideas and results, sometimes in a well-developed form, and other times as flashes into the anatomy of the workings of a unique mind.

Keywords

predicate logic type theory natural calculi cut theorem Paul Bernays

Authors and affiliations

  • Jan von Plato
    • 1
  1. 1.Department of PhilosophyUniversity of HelsinkiHelsinkiFinland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42120-9
  • Copyright Information Springer International Publishing Switzerland 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-42119-3
  • Online ISBN 978-3-319-42120-9
  • Series Print ISSN 2196-8810
  • Series Online ISSN 2196-8829
  • Buy this book on publisher's site