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.

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

Autorentext

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

Inhalt

Preface.- Chapter 1. Introduction (Gerhard Heinzmann).- Chapter 2. N.N (Kuno Lorenz).- Chapter 3. Some contributions of Lorenzen to constructive mathematics and an application to constructive measure theory (Thierry Coquand).- Chapter 4. Lorenzen's work on lattice-groups and divisibility theory. From a classical celebrated result to a relevant constructive rewriting (Henri Lombardi).- Chapter 5. Lorenzen's reshaping of Krull's Fundamentalsatz for integral domains (19391953) (Stefan Neuwirth).- Chapter 6. Extension by Conservation (Peter M. Schuster).- Chapter 7. Modern set theory and Lorenzen's critique of actual infinity (Carolin Antos).- Chapter 8. The main problem of Grundlagenforschung (Jan von Plato).- Chapter 9. Lorenzen's consistency proof and Hilbert's larger programme (Reinhard Kahle).- Chapter 10. From Lorenzen's dialogue game to game semantics for substructural logics (Christian Fermüller).- Chapter 11. A Constructive Examination of a Russell-style Ramified Type Theory(Erik Palmgren).- Chapter 12. A circularity puzzle within the operative justification of logic and mathematics and a way out (Shahid Rahman). <p