Peter Zahn (mathematician)

Peter Zahn,
TH Darmstadt, 1995

Peter Zahn (born June 4, 1930 in Leipzig ) is a German mathematician and logician and retired professor in the mathematics department of the Technical University of Darmstadt .

Life

After graduating from the Leibniz-Gymnasium in 1948, Peter Zahn began an agricultural apprenticeship, which he completed in 1950 with the journeyman's examination. After two years of salaried employment, he began to study teaching at the Schwäbisch Gmünd Pedagogical Institute in the 1952 summer semester.

After one semester he switched to the University of Tübingen with the subjects mathematics , biology and philosophy and graduated in 1959 with the first state examination for teaching at grammar schools . After his legal clerkship in Tübingen, which he completed with the second state examination in 1961 , he was a grammar school teacher in Spaichingen for five years . During this time he did his doctorate with Kurt Schütte and Hellmuth Kneser at the Eberhard Karls University in Tübingen and completed his doctorate in 1965 with the dissertation An Introduction of Real Numbers in the Framework of Operational Logic without the distinction between language layers .

From 1966 to 1971 Peter Zahn taught primarily mathematics at the State Engineering School in Meschede , but also gave seminars in philosophy and music.

In 1971 he was hired as a university professor at the TH-Darmstadt . With his work The Follow-Up Relationship in Semi-Formalisms , published in 1972 , he received his habilitation in 1973 in Darmstadt. The speakers were Detlef Laugwitz , Paul Lorenzen and Kurt Schütte. Then he was appointed private lecturer . In 1989 he was appointed associate professor at the TU Darmstadt. He retired in 1995.

Act

Peter Zahn's particular scientific interest is in the foundations and philosophy of logic and mathematics , especially methodological constructivism . With Paul Lorenzen he was in a decades-long exchange, mostly by letter. His areas of work included:

• School mathematics and didactics.
• Constructive (predictive) justifications of parts of measure theory, functional analysis and non-standard analysis (i.e. avoiding demanding set theoretical means).
• Investigation of the initial problem to justify the logic by introducing assertion games . (Can arguments be proven to be reliable using arguments? How, if necessary?)
• (Re) construction and logical treatment of languages ​​in which non-mathematical statements (assertion sentences) also occur, later also of languages ​​of higher levels in which indexical expressions and object variables (in the sense of W. v. O. Quine ) occur, and in which, in addition to the quantification of the insertion, the quantification of the object can also be carried out.

Since his retirement, his lectures at the Ernst Schröder Center , the philosophical tea group at the TU Darmstadt , and the Darmstadt Ontologenkreis have always been well attended and discussed.

Trivia

During his time at the State Engineering School in Meschede , Peter Zahn played together with students in a jazz band, first the clarinet, later the saxophone. In recent years he has illustrated several children's books by his wife Ingeborg Zahn.

literature

• Peter Zahn. Hit list in the TU bibliography. University and State Library Darmstadt, accessed on May 27, 2014 . 

Fonts

1. ↑ Peter Zahn: An introduction to real numbers in operational mathematics without differentiating between language layers . In: Mathematical Seminar Giessen (Ed.): Messages from the Mathematical Seminar Giessen . No. 72 . Ed. Of the Math. Seminar, Giessen 1967.
2. ↑ Peter Zahn: The consequence relationship in Halbformalismen . Habilitation thesis (132 pages). In: TH-Darmstadt , Department of Mathematics (Ed.): Preprint . tape 27 . Darmstadt 1972.
3. ↑ Peter Zahn: Proof in mathematics class . Wissenschaftliche Buchgesellschaft, Darmstadt 1978, ISBN 978-3-534-07721-2 (book, 233 pages).
4. ↑ Peter Zahn: A constructive way to measure theory and functional analysis . Wissenschaftliche Buchgesellschaft, Darmstadt 1978, ISBN 978-3-534-07767-0 (book, 350 pages).
5. ↑ Peter Zahn: A predicative approach to nonstandard mathematics . In: Zeitschr. f. Math. Logic and Fundamentals of the Math. Volume 33 , 1987, pp. 85-98 , doi : 10.1002 / malq.1987033011 (English).
6. ^ Peter Zahn: Supplements to the article: A predicative approach to nonstandard mathematics . In: Zeitschr. f. Math. Logic and Foundations of Math. 1989.
7. ↑ Peter Zahn: A Nonstandard Delta Function in a Predicative Theory . In: Mathematical Logic Quarterly . tape 41 , 1995, pp. 257-260 (English).
8. ↑ Peter Zahn: An argumentative way to logic . Book, 212 pages. Scientific Book Society, Darmstadt 1982, ISBN 978-3-534-08751-8 .
9. ↑ Peter Zahn: Thoughts on the pragmatic justification of logic and mathematics . In: Herbert Stachowiak (Ed.): Pragmatik IV . Meiner, 1992, ISBN 3-7873-0660-9 .
10. ↑ Peter Zahn: A normative model of classical reasoning in higher order languages . In: Synthesis . tape 148 , 2006, pp. 309-343 (English).
11. ↑ Peter Zahn: Ontology and Semiotics. (PDF) (No longer available online.) October 9, 2013, formerly in the original ; Retrieved June 10, 2014 .  ( Page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice.    

Individual evidence

1. ↑ Peter Zahn. (php) In: Mathematics Genealogy Project. Retrieved May 16, 2014 . 
2. ↑ ^{a b} The State Engineering School Meschede is now part of the University of Paderborn
3. ↑ Fred Richman: Peter Zahn: A constructive way to measure theory and functional analysis . Book review. In: Journal of Symbolic Logic . tape 47 , no. September 3 , 1982.
4. ↑ Siegfried Gottwald: Peter Zahn: An argumentative path to logic . Book review. In: Mathematical Reviews . 1984.
5. ↑ z. B. Inge Zahn, Peter Zahn (illustrated): Lili Mähi-Lili: mysterious stories for children . Ed .: Inge Zahn, Peter Zahn. 1st edition. Ed. Blauer Feder, Dieburg 2008, ISBN 978-3-9808645-7-2 .