Paul Lorenzen
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| Paul Lorenzen | |
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| Born | March 24, 1915 |
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| Died | October 1, 1994 |
| Fields | Philosophy, Mathematics |
Paul Lorenzen (born March 24, 1915 in Kiel, Germany - died October 1, 1994 in Göttingen, Germany) was a philosopher and mathematician.
As a founder of the Erlangen School (with Wilhelm Kamlah) and the inventor of game semantics (with Kuno Lorenz) he was a famous German philosopher of the 20th century.
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[edit] Biography
Lorenzen studied with David Hilbert as a school boy and he was one of Hasse's students at the University of Göttingen until his promotion in 1938. He became pupil of Krull in University of Bonn. His main work was on the foundations of mathematics, in proof theory. He created and modified constructive mathematics. Lorenzen taught at Stanford, the University of Texas, and Boston University in the USA.
[edit] Theory
Lorenzen came in 1962 to University of Erlangen (South Germany) and founded the school of constructivist philosophy there. He wrote with Kamlah the famous book Logical Propaedeutic ("Logische Propädeutik") and worked on game semantics ("Dialogische Logik") with Kuno Lorenz. With Peter Janich he invented protophysics of time and space. He developed constructivist logic, constructivist type theory and constructivist analysis.
Lorenzen's work on calculus Differential and Integral was dedicated to Hermann Weyl. Lorenzen used Weyl's technique to develop a predicative analysis, which can reconstruct classical analysis, without the principle of excluded middle or the Axiom of Choice.
In the theory of geometry and physics, Lorenzen was influenced by Hugo Dingler. He followed Dingler in building up geometry and physics out of primitive operations. Lorenzen followed Dingler in having doubts about general relativity, believing that Maxwell's equations would need to be modified.
Lorenzen was also influenced by Wilhelm Dilthey's hermeneutics, and liked to quote Dilthey's saying that knowledge cannot go behind life. Dilthey's Lebensphilosophie was the description of the setting in ordinary experience in which we construct the abstractions of mathematics and physics.
Lorenzen took modal (incl. normative) logic as a base of technical and political science and research.
[edit] Major works
- Paul Lorenzen, Normative Logic and Ethics, Mannheim/Zürich 1969.
- Paul Lorenzen, Lehrbuch der konstruktiven Wissenschaftstheorie.
- Paul Lorenzen, Differential and integral;: A constructive introduction to classical analysis.
- Paul Lorenzen, Karl Richard Pavlovic (Translator), Constructive Philosophy. The University of Massachusetts Press, Amherst 1987.
- deductive presentation of constructivist philosophy, mathematics and protophysics.
- Paul Lorenzen, Formal Logic (Synthese Library (Hardcover)) (Hardcover - July 1964).
- Wilhelm Kamlah, Paul Lorenzen: Logical Propaedeutic: Pre-School of Reasonable Discourse.
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- Diane Loring Souvaine, Paul Lorenzen and constructive mathematics.
