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The Foundational Debate

Complexity and Constructivity in Mathematics and Physics

  • Book
  • © 1995

Overview

Editors:
  1. Werner Depauli-Schimanovich

    1. University of Vienna, Austria

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  2. Eckehart Köhler

    1. University of Vienna, Austria

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  3. Friedrich Stadler

    1. University of Vienna, Austria
      Institut ‘Wiener Kreis’, Vienna, Austria

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Part of the book series: Vienna Circle Institute Yearbook (VCIY, volume 3)

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Table of contents (28 chapters)

  1. Front Matter

    Pages I-XIV
    Download chapter PDF

  2. Articles

    2. Complexity

      1. How Far Can We Formalize Language Games?
        • Rohit Parikh
        Pages 89-100
      2. What is a Random String?
        • Cristian Calude
        Pages 101-113
      3. Strong Determinism vs. Computability
        • Cristian Calude, Douglas I. Campbell, Karl Svozil, Doru Ştefănescu
        Pages 115-131
      4. Capturing Relativized Complexity Classes with Lindström Quantifiers
        • Janos A. Makowsky
        Pages 133-140

    3. Constructivism

      1. Why Constructive Mathematics?
        • Dirk van Dalen
        Pages 141-157
      2. Hypothetical Extensions of Constructive Mathematics
        • Peter H. Krauss
        Pages 159-174
      3. Constructions as the Subject Matter of Mathematics
        • Pavel Tichý
        Pages 175-185
      4. Verificationism Then and Now
        • Per Martin-Löf
        Pages 187-196
      5. Logic and Mathematics
        • Jan Wolénski
        Pages 197-210
      6. A Connection between Leibniz’ Infinitely Small Quantities and the Analytical Hierarchy
        • Karel Čuda
        Pages 211-218
      7. Extensional Equality in the Classical Theory of Types
        • William W. Tait
        Pages 219-234
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Keywords

About this book

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics.
This `foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics.

Editors and Affiliations

  • University of Vienna, Austria

    Werner Depauli-Schimanovich, Eckehart Köhler, Friedrich Stadler

  • Institut ‘Wiener Kreis’, Vienna, Austria

    Friedrich Stadler

Bibliographic Information

  • Book Title: The Foundational Debate

  • Book Subtitle: Complexity and Constructivity in Mathematics and Physics

  • Editors: Werner Depauli-Schimanovich, Eckehart Köhler, Friedrich Stadler

  • Series Title: Vienna Circle Institute Yearbook

  • DOI: https://doi.org/10.1007/978-94-017-3327-4

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1995

  • Hardcover ISBN: 978-0-7923-3737-9Published: 30 September 1995

  • Softcover ISBN: 978-90-481-4617-8Published: 04 December 2010

  • eBook ISBN: 978-94-017-3327-4Published: 14 March 2013

  • Series ISSN: 0929-6328

  • Series E-ISSN: 2215-1818

  • Edition Number: 1

  • Number of Pages: XIV, 354

  • Topics: Logic, Mathematical Logic and Foundations, Quantum Physics, Artificial Intelligence, History, general

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