Paul Lorenzen -- Mathematician and Logician

1. Front Matter

   Pages i-xii

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2. Paul Lorenzens Weg von der Mathematik zur Philosophie - Persönliche Erinnerungen

   • Kuno Lorenz

   Pages 1-9Open Access

3. Operation and Predicativity: Lorenzen’s Approach to Arithmetic

   • Gerhard Heinzmann

   Pages 11-22Open Access

4. Conceptions of Infinity and Set in Lorenzen’s Operationist System

   • Carolin Antos

   Pages 23-46Open Access

5. Lorenzen and Constructive Mathematics

   • Thierry Coquand

   Pages 47-61Open Access

6. Lorenzen Between Gentzen and Schütte

   • Reinhard Kahle, Isabel Oitavem

   Pages 63-76Open Access

7. Syntax for Semantics: Krull’s Maximal Ideal Theorem

   • Peter Schuster, Daniel Wessel

   Pages 77-102Open Access

8. Regular Entailment Relations

   • Thierry Coquand, Henri Lombardi, Stefan Neuwirth

   Pages 103-114Open Access

9. Connecting Sequent Calculi with Lorenzen-Style Dialogue Games

   • Christian G. Fermüller

   Pages 115-141Open Access

10. Lorenzen’s Reshaping of Krull’s Fundamentalsatz for Integral Domains (1938–1953)

    • Stefan Neuwirth

    Pages 143-183Open Access

11. Lorenzen’s Correspondence with Hasse, Krull, and Aubert, Together with Some Relevant Documents

    • Stefan Neuwirth

    Pages 185-268Open Access

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

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

  Gerhard Heinzmann

• Fachbereich Philosophie, Universitat Konstanz, Konstanz, Germany

  Gereon Wolters

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 academia.edu and ResearchGate.