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oapen-20.500.12657-507032021-10-06T02:43:27Z Paul Lorenzen -- Mathematician and Logician Heinzmann, Gerhard Wolters, Gereon 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 bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBB Philosophy of mathematics bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBX History of mathematics bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBC Mathematical foundations 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. 2021-10-05T14:04:55Z 2021-10-05T14:04:55Z 2021 book ONIX_20211005_9783030658243_5 9783030658243 https://library.oapen.org/handle/20.500.12657/50703 eng Logic, Epistemology, and the Unity of Science application/pdf n/a 978-3-030-65824-3.pdf https://www.springer.com/9789811645785 Springer Nature Springer 10.1007/978-3-030-65824-3 10.1007/978-3-030-65824-3 6c6992af-b843-4f46-859c-f6e9998e40d5 9783030658243 Springer 51 268 open access
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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.
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