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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.

Philosophy of mathematics --- History of mathematics --- Mathematical foundations --- 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 --- Mathematics --- Mathematics. --- History. --- Mathematical logic. --- Philosophy of Mathematics. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Philosophy. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Math --- Science --- Logic of mathematics --- Mathematics, Logic of