Ernst Kleinert
Ernst Kleinert (born March 23, 1952 in Düren ) is a German mathematician and philosopher .
Become
After the first four years at what was then the Düren-Ost elementary school, he completed his Abitur at the Stiftisches Gymnasium Düren . He then completed a degree in mathematics in Cologne. Kleinert's dissertation (1981) dealt with the topic of the unit theory of integer group rings . Later he was visiting professor a. a. in Edmonton / Canada. He is currently teaching as a private lecturer at the University of Hamburg . Kleinert's mathematical interest is linear algebra and number theory.
The work
Ernst Kleinert's work includes both mathematical and mathematical-philosophical work.
Philosophy of mathematics
Kleinert's main work in the field of philosophy of mathematics is mathematics for philosophers . It is a large-scale overview of the most important mathematical disciplines, each derived from their axiomatic foundations. Several specifically philosophical topics are addressed: mathematics and its forms of visualization, mathematics as a language game, Carnap's quasian analysis, categorical structures in language and logic, mereology , space theory according to Whitehead , categorical semantics. Overall, Kleinert's aim is to show how all basic mathematical disciplines can be derived from what he calls the “categorical system” of humans.
In further mathematical-philosophical essays Kleinert develops his concept of the categorical system further, whereby he repeatedly shows both the comprehensive and the specific limitation of mathematical thinking. This is how he writes in mathematics, script and calculation :
- “The symbol was once a triumph of the spirit, which emancipated it from what was hic et nunc by being able to visualize objects that are not present at any time. At a higher level, every calculation relieves the mind of hard work and sets it free for more essential tasks. Where, of course, he does not see such, the hard work is only increased; the blossoming life of the calculus of its own makes one think more of the sorcerer's apprentice, to whom the broom has fallen into his hands, but who knows nothing about a master; and one can doubt that his mind is on the rise to something more essential. "
With such reflections, Kleinert energetically limits the claim to mathematical hegemony and directs his gaze to the other side of mathematical thinking. In the context of philosophy, Kleinert's theory occupies an outsider position insofar as it was developed consistently from the perspective of the mathematician.
In Categories in Philosophy and Mathematics in Is There Safe Knowledge , Ed. Michael Rahnfeld, Leipziger Universitätsverlag, 2006, Ernst Kleinert dedicates himself to the concept of the category as a philosophical and mathematical term: Aristotle and Kant examined the universal structures of judgment and thus in their theory of categories - in ontological terms - the world in general; Mathematical category theory deals with the universal structures within mathematics by examining the general properties of a mathematical structure in terms of their relationships to other structures. On the basis of the theory of categories, Kleinert outlines a program for a philosophy of mathematics .
literature
- Units in Skew Fields . Birkhäuser, 2000, ISBN 3-7643-6293-6 .
- Contributions to a philosophy of mathematics . Leipzig University Press, 2003
- About associativity and commutativity . Math. Semester reports 2, 2003, 29–43
- Categories in Philosophy and Mathematics . Hamburg Contributions 199, 2004 PS.gz
- Combinatorics of Quantifiers . Hamburg Contributions 200, 2004 PS.gz
- On the Reducibility of Relations: Variations on a Theme of Peirce . Hamburg Contributions 201, 2004 PS.gz ; in: Transactions of the Charles S. Peirce Society . Volume 43, No. 3, 2007, pp. 509-520
- Mathematics for Philosophers . Leipzig University Press, 2004
- The categorical system and the place of mathematics . 2005; Hamburg contributions 246, 2006 PDF
- Three studies on the structure of mathematics ( On linearity , On two and duality , On some strategies of mathematical thinking ). Hamburg contributions 229, Dec. 2005 PDF
- What does logical validity mean? . Hamburg contributions 247, 2006 PDF
- On the Restriction and Corestriction of Algebras over Number Fields . 2006; Hamburg contributions 270, 2007 PDF
- Of numbers and figures . Hamburg contributions 256, 2006 PDF
- Categories in Mathematics and Philosophy . In: M. Rahnfeld (Ed.): Is there any reliable knowledge? . Leipzig 2006
- Mathematics, writing and calculation (PDF; 199 kB). Hamburg Contributions 274, 2007
- Mathematics and Psychoanalysis (PDF; 339 kB): Attempts at an approximation. Frege and Freud on the negation . Hamburg Contributions 316, Sept. 2008
- Mathematics and Determinism (PDF; 209 kB). Hamburg Posts 334, May 2009
- About inside and outside (PDF; 375 kB): philosophical-mathematical forays . Hamburg Contributions 378, May 2010
- Plato's unwritten teaching (PDF; 223 kB) and today's mathematics . Hamburg Contributions 388, Sept. 2010
Web link
personal data | |
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SURNAME | Kleinert, Ernst |
BRIEF DESCRIPTION | German mathematician and philosopher |
DATE OF BIRTH | March 23, 1952 |
PLACE OF BIRTH | Düren |