Paul Lorenzen (March 24, 1915 – October 1, 1994) was a German philosopher and mathematician, founder of the Erlangen School (with Wilhelm Kamlah) and inventor of

game semantics Game semantics (german: dialogische Logik, translated as ''dialogical logic'') is an approach to Formal semantics (logic), formal semantics that grounds the concepts of truth or Validity (logic), validity on game theory, game-theoretic concepts, su ...

(with Kuno Lorenz).

Biography

Lorenzen studied at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

until he earned his PhD there in 1938 under Helmut Hasse with a thesis titled ''Zur Abstrakten Begründung der multiplikativen Idealtheorie''. In 1939, he became an assistant to

Wolfgang Krull Wolfgang Krull (26 August 1899 – 12 April 1971) was a German mathematician who made fundamental contributions to commutative algebra, introducing concepts that are now central to the subject. Krull was born and went to school in Baden-Baden. H ...

at the

University of Bonn The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine U ...

. His main work was on the foundations of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

—

proof theory Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four correspo ...

. He created and modified

constructive mathematics In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove th ...

. Lorenzen taught at

Stanford Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considere ...

, the

University of Texas The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...

, and

Boston University Boston University (BU) is a private research university in Boston, Massachusetts. The university is nonsectarian, but has a historical affiliation with the United Methodist Church. It was founded in 1839 by Methodists with its original campu ...

in the USA. He was John Locke Lecturer in 1967/1968.

Theory

Lorenzen came in 1962 to

University of Erlangen A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...

(South Germany) and founded the

Erlangen School Neo-Lutheranism was a 19th-century revival movement within Lutheranism which began with the Pietist-driven '' Erweckung,'' or ''Awakening'', and developed in reaction against theological rationalism and pietism. This movement followed the Old Lu ...

epistemological constructivism Constructivism is a view in the philosophy of science that maintains that scientific knowledge is constructed by the scientific community, which seeks to measure and construct models of the natural world. According to the constructivist, natur ...

there. He wrote with Wilhelm Kamlah the famous book ''Logical Propaedeutic'' ("Logische Propädeutik") and worked on

(''Dialogische Logik'') with Kuno Lorenz. With

Peter Janich Peter Janich (4 January 1942 – 4 September 2016) was a professor of philosophy at the University of Marburg. He was born in Munich. Janich studied physics, philosophy and psychology at the Universities of Erlangen and Hamburg. He attained a doct ...

he invented ''protophysics'' of time and space. He developed

constructive logic Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems o ...

constructive type theory Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics. Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician a ...

and

constructive analysis In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics. This contrasts with ''classical analysis'', which (in this context) simply means analysis done according to the (more comm ...

. Lorenzen's work on calculus ''Differential and Integral'' was dedicated to

Hermann Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...

. Lorenzen used Weyl's technique to develop a predicative analysis, which can reconstruct

classical analysis Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied in ...

, without the principle of excluded middle or the

axiom of choice In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that ''a Cartesian product of a collection of non-empty sets is non-empty''. Informally put, the axiom of choice says that given any collectio ...

. He worked also on

Gerhard Gentzen Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died ...

cut elimination The cut-elimination theorem (or Gentzen's ''Hauptsatz'') is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen in his landmark 1934 paper "Investigations in Logical Deduction" for ...

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 Steven Weinberg (; May 3, 1933 – July 23, 2021) was 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 interactio ...

(Gravitation and Cosmology, 1972) for his doubts about geometrical elements of

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

, believing that

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...

are to be modified by general relativity instate. Lorenzen was also influenced by

Wilhelm Dilthey Wilhelm Dilthey (; ; 19 November 1833 – 1 October 1911) was a German historian, psychologist, sociologist, and hermeneutic philosopher, who held G. W. F. Hegel's Chair in Philosophy at the University of Berlin. As a polymathic philosopher, w ...

hermeneutics Hermeneutics () is the theory and methodology of interpretation, especially the interpretation of biblical texts, wisdom literature, and philosophical texts. Hermeneutics is more than interpretative principles or methods used when immediate c ...

, and liked to quote Dilthey's saying that knowledge cannot go behind life. Dilthey's ''

Lebensphilosophie (; meaning 'philosophy of life') was a dominant philosophical movement of German-speaking countries in the late 19th and early 20th centuries, which had developed out of German Romanticism. emphasised the meaning, value and purpose of life as ...

'' 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 Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, along with aesthetics, concerns m ...

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 (Translator), ''Constructive Philosophy'', The

University of Massachusetts Press The University of Massachusetts Press is a university press that is part of the University of Massachusetts Amherst. The press was founded in 1963, publishing scholarly books and non-fiction. The press imprint is overseen by an interdisciplinar ...

, Amherst, 1987.

References

* Wilhelm Kamlah, Paul Lorenzen, ''Logical Propaedeutic: Pre-School of Reasonable Discourse'', Washington, D.C.: University Press of America, 1984. * Diane Loring Souvaine, ''Paul Lorenzen and Constructive Mathematics'', 1980.

External links

*
Books from and about Lorenzen at Deutsche National Bibliothek
{{DEFAULTSORT:Lorenzen, Paul 1915 births 1994 deaths 20th-century German mathematicians 20th-century German philosophers Continental philosophers German logicians Proof theorists Philosophers of language University of Bonn alumni German male writers Relativity critics