Paul Lorenzen (born March 24, 1915 in Kiel, Germany) is a philosopher and mathematician. March 24 is the 83rd day of the year in the Gregorian Calendar (84th in Leap years). ... 1915 was a common year starting on Friday (see link for calendar). ... Statistics State: Schleswig-Holstein District: Independent city Area: 113. ... A philosopher is a person devoted to studying and producing results in philosophy. ... A mathematician is a person whose area of study and research is mathematics. ...

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. Game semantics is an approach to the semantics of logic that bases the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player. ...

Biography

Lorenzen studied at David Hilbert as a school boy and he was one of Hasse's students at the University of Göttingen until his promotion 1938. He become 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. David Hilbert David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ... Helmut Hasse (pronounced HAHS uh) (25 August 1898- 26 December 1979) 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 (Hasse principle), and to local zeta functions. ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... 1938 was a common year starting on Saturday (link will take you to calendar). ... The main building, viewed from the Hofgarten. ... Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... Proof theory, studied as a branch of mathematical logic, represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ... In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct) a mathematical object to prove that it exists. ...

Theory

Lorenzen came 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. Erlangen is a German city in Middle Franconia. ... Game semantics is an approach to the semantics of logic that bases the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player. ... Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ... Intuitionistic Type Theory, or Constructive Type Theory, or Martin-Löf Type Theory or just Type Theory (with capital letters) is at the same time a functional programming language, a logic and a set theory based on the principles of mathematical constructivism. ... In mathematics, constructive analysis is mathematical analysis done according to the principles of constructivist mathematics. ...

Lorenzen took modal (incl. normative) logic as a base of technical and political science and research. Modal logic, or (less commonly) intensional logic is the branch of logic that deals with sentences that are qualified by modalities such as can, could, might, may, must, possibly, and necessarily, and others. ...

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

---

• Diane Loring Souvaine: Paul Lorenzen and constructive mathematics

See also

External links

just some basic info books from and about Lorenzen at ddb in germany