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Paul Lorenzen -- Mathematician and Logician
Beschreibung:
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.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. Lorenzeṇ’s work on lattice-groups and divisibility theory. From a classical celebrated result to a relevant constructive rewriting (Henri Lombardi).- Chapter 5. Lorenzeṇ’s reshaping of Krull’s Fundamentalsatz for integral domains (1939–1953) (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).