Paul Lorenzen
Encyclopedia
Paul Lorenzen 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.
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.
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.
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
As a founder of the Erlangen School (with Wilhelm Kamlah) and the inventor of game semantics
Game semantics
Game semantics is an approach to formal semantics that grounds the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player, somewhat resembling Socratic dialogues or medieval theory of Obligationes. In the late 1950s Paul Lorenzen was the...
(with Kuno Lorenz
Kuno Lorenz
Kuno Lorenz is a German philosopher. He developed a philosophy of dialogue, in connection with the pragmatic theory of action of the Erlangen constructivist school...
) he was a famous German philosopher of the 20th century.
Biography
Lorenzen studied with David HilbertDavid Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
as a schoolboy and he was one of Hasse
Helmut Hasse
Helmut Hasse was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local classfield theory and diophantine geometry , and to local zeta functions.-Life:He was born in Kassel, and died in...
's students at the University of Göttingen until his promotion in 1938. He became pupil of Krull in University of Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
. His main work was on the foundations of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, in proof theory
Proof theory
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed...
. He created and modified constructive mathematics
Constructivism (mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption, one still has not found the object and therefore not proved its...
. Lorenzen taught at Stanford, the University of Texas, and Boston University in the USA. He was John Locke Lecturer
John Locke lectures
The John Locke Lectures are a series of annual lectures in philosophy given at the University of Oxford. They are one of the world's most prestigious academic lecture series, comparable to the Gifford Lectures given in Scottish universities...
in 1967/1968.
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
Game semantics
Game semantics is an approach to formal semantics that grounds the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player, somewhat resembling Socratic dialogues or medieval theory of Obligationes. In the late 1950s Paul Lorenzen was the...
(Dialogische Logik) with Kuno Lorenz. With Peter Janich
Peter Janich
Peter Janich is a professor of philosophy at the University of Marburg. Janich studied physics, philosophy and psychology at the Universities of Erlangen and Hamburg. He attained a doctorate in philosophy in 1969 and during 1969/70 was a guest lecturer at the University of Texas in Austin...
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
Hermann Weyl
Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
. Lorenzen used Weyl's technique to develop a predicative
Predicative
Predicative may mean:* Predicative * Predicative * Lacking impredicativity...
analysis, which can reconstruct classical analysis, without the principle of excluded middle or the Axiom of Choice. He worked also on Gerhard Gentzen
Gerhard Gentzen
Gerhard Karl Erich Gentzen was a German mathematician and logician. He had his major contributions in the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus...
'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
Hugo Dingler
Hugo Albert Emil Hermann Dingler . Dingler was a German scientist and philosopher.-Life:...
. He followed Dingler in building up geometry and physics out of primitive operations. Lorenzen took an early interpretation of Steven Weinberg
Steven Weinberg
Steven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
(Gravitation and Cosmology, 1972) for his doubts about geometrical elements of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, believing that Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
are to be modified by general relativity instate.
Lorenzen was also influenced by Wilhelm Dilthey
Wilhelm Dilthey
Wilhelm Dilthey was a German historian, psychologist, sociologist and hermeneutic philosopher, who held Hegel's Chair in Philosophy at the University of Berlin. As a polymathic philosopher, working in a modern research university, Dilthey's research interests revolved around questions of...
'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
John Locke lectures
The John Locke Lectures are a series of annual lectures in philosophy given at the University of Oxford. They are one of the world's most prestigious academic lecture series, comparable to the Gifford Lectures given in Scottish universities...
he invented normative Logic as a base on ethics
Ethics
Ethics, also known as moral philosophy, is a branch of philosophy that addresses questions about morality—that is, concepts such as good and evil, right and wrong, virtue and vice, justice and crime, etc.Major branches of ethics include:...
and political argumentation.
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.
See also
- Wilhelm Kamlah, Paul Lorenzen: Logical Propaedeutic: Pre-School of Reasonable Discourse.
- Diane Loring Souvaine, Paul Lorenzen and Constructive Mathematics.