# Paul Lorenzen : biography

**Paul Lorenzen** (March 24, 1915 – October 1, 1994) 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.

## Theory

Lorenzen came in 1962 to University of Erlangen (South Germany) and founded the Erlangen School of epistemological constructivism 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 constructive logic, constructive type theory and constructive 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. He worked also on Gerhard Gentzen's cut elimination to find a way to continue Hilbert's program after the results of Gödel.

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 took an early interpretation of Steven Weinberg (Gravitation and Cosmology, 1972) for his doubts about geometrical elements of general relativity, believing that Maxwell's equations are to be modified by general relativity instate.

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.

As John Locke Lecturer he invented normative Logic as a base on ethics and political argumentation.

## Biography

Lorenzen studied with David Hilbert as a schoolboy 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. He was John Locke Lecturer in 1967/1968.

## Major works

- Paul Lorenzen, Frederick J. Crosson (Translator),
*Formal Logic*, Springer, New York, July 1964. - Paul Lorenzen,
*Normative Logic and Ethics*, Mannheim/Zürich, 1969. - Paul Lorenzen, John Bacon (Translator),
*Differential and Integral: A constructive introduction to classical analysis*, The University of Texas Press, Austin, 1971. - Paul Lorenzen,
*Lehrbuch der konstruktiven Wissenschaftstheorie*, Mannheim/Zürich, 1984. - Paul Lorenzen, Karl Richard Pavlovic (Trans.),
*Constructive Philosophy*, The University of Massachusetts Press, Amherst, 1987.