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  • Book
  • Open Access
  • © 2021

Paul Lorenzen -- Mathematician and Logician

  • Details an original approach to the history of logic and mathematics

  • Contributes to debates on proof-theoretic semantics, databank management, and stochastics

  • Features papers from a meeting at the University of Konstanz

Part of the book series: Logic, Epistemology, and the Unity of Science (LEUS, volume 51)

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  • ISBN: 978-3-030-65823-6
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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
  2. Operation and Predicativity: Lorenzen’s Approach to Arithmetic

    • Gerhard Heinzmann
    Pages 11-22Open Access
  3. Lorenzen and Constructive Mathematics

    • Thierry Coquand
    Pages 47-61Open Access
  4. Lorenzen Between Gentzen and Schütte

    • Reinhard Kahle, Isabel Oitavem
    Pages 63-76Open Access
  5. Syntax for Semantics: Krull’s Maximal Ideal Theorem

    • Peter Schuster, Daniel Wessel
    Pages 77-102Open Access
  6. Regular Entailment Relations

    • Thierry Coquand, Henri Lombardi, Stefan Neuwirth
    Pages 103-114Open Access
  7. Connecting Sequent Calculi with Lorenzen-Style Dialogue Games

    • Christian G. Fermüller
    Pages 115-141Open Access

About this book

This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics.

Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics.

Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.


  • Lorenzen on Constructive Mathematics
  • Application to Constructive Measure Theory
  • Lorenzeṇ’s Work on Lattice-groups and Divisibility Theory
  • Krull’s Fundamentalsatz for Integral Domains
  • Modern Set Theory and Lorenzen’s Critique of Actual Infinity
  • Grundlagenforschung
  • Lorenzen’s Consistency Proof and Hilbert’s Larger Programme
  • Lorenzen's Dialogue Game
  • Game Semantics for Substructural Logics
  • Constructive Examination of a Russell-style Ramified Type Theory
  • Operative Justification of Logic and Mathematics
  • Lorenzen on Proof-theoretic Semantics
  • Lorenzen on Databank Management
  • Lorenzen on Stochastics
  • Russell-style Ramified Type Theory
  • Lorenzen and Erlangen School of Methodical Constructivism

Editors and Affiliations

  • Laboratoire de Philosophie et d'Histoire, Universite de Lorraine, NANCY CEDEX, France

    Gerhard Heinzmann

  • Fachbereich Philosophie, Universitat Konstanz, Konstanz, Germany

    Gereon Wolters

About the editors

Gerhard Heinzmann is Professor of Philosophy of Mathematics and Logic in the Department of Philosophy at the University of Lorraine at Nancy (France). Founder of the Research Center Laboratoire d'Histoire des Sciences et de Philosophie - Archives Henri –Poincaré (UMR 7117 of the CNRS), former Director of the Lorrain Institute for Humanities and Social Sciences (MSH, 2007-2014), founder of the journal Philosophia Scientiae, he is the editor of the Publications of the Henri-Poincaré Archives (Birkhäuser). Author of numerous articles and books on the philosophy of Henri Poincaré, Ferdinand Gonseth, Jean Cavaillès and Paul Bernays, among them Zwischen Objektkonstruktion und Strukturanalyse. Zur Philosophie der Mathematik bei Henri Poincaré (1995) ; L’intuition épistémique. Une approche pragmatique du contexte de justification en mathématiques et en philosophie (2013), he was the President of the organizing Committee of the 14th International Congress of Logic, Methodology and Philosophy of Science (Nancy 2011), and is the President of the International Academy for Philosophy of Science, Brussels; he even is member of the Academia Europaea and the European Academy of Sciences.

Gereon Wolters studied philosophy and mathematics at the universities of Innsbruck, Tübingen and Kiel. His main research areas are history and philosophy of science (Ernst Mach, philosophy of biology, logical empiricism), philosophy during National Socialism and World War I, science and religion, consequences of English as lingua franca in the humanities, philosophy of enlightenment. Visiting lecturer at the University of Zurich (1985-2008) and full professor at the University of Constance (since 1988, currently Emeritus), where he has founded and directed the Philosophisches Archiv. He was research fellow at the Center for Philosophy of Science  of the University of Pittsburgh (1996-97), at the Netherlands Institute for Advanced Study (2008/09) and at the He^Dritte Reich< (2004); Ambivalenz und Konflikt. Katholische Kirche und Evolutionstheorie (2010);  Globalizzazione del bene? (2015). - For more publications see his sites on and ResearchGate.

Bibliographic Information

Buying options

Hardcover Book USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-65823-6
  • Dispatched in 3 to 5 business days
  • Exclusive offer for individuals only
  • Free shipping worldwide
    See shipping information.
  • Tax calculation will be finalised during checkout