Ernst Kleinert

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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 .

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personal data
SURNAME Kleinert, Ernst
BRIEF DESCRIPTION German mathematician and philosopher
DATE OF BIRTH March 23, 1952
PLACE OF BIRTH Düren