Ernst Cassirer’s Philosophy of Mathematics – A Cultural Philosophy of Mathematics at the Beginning of the 20th Century.
Mathematics
Theoretical Philosophy
Final Report Abstract
The DFG project “Ernst Cassirers Philosophie der Mathematik – Eine Kulturphilosophie der Mathematik am Beginn des 20. Jahrhunderts” aimed on the one hand to shed light on the interrelationship between Cassirer's philosophy of mathematics and his much more comprehensive philosophy of culture, and on the other hand to bring current research on Cassirer's philosophy of culture into fruitful exchange with research on his philosophy of mathematics. Both were addressed in the project as follows: Firstly, the dissertation written by project researcher Daniel Koenig, Mathematik als Erkenntnisform. Ernst Cassirer's Philosophie der Mathematik und ihre paradigmatische Bedeutung für die Philosophie der symbolischen Formen shows that Cassirer's definition of mathematics as a form of theoretical knowledge both provides promising insights into the philosophy of mathematics from today's perspective and is of paradigmatic importance for his broader philosophy of culture. Accordingly, Cassirer's philosophy of mathematics was reconstructed in detail in this work and presented in its interrelationship with his philosophy of culture. However, Cassirer's engagement with mathematics is not only interesting for the philosophy of mathematics, but also for research on Cassirer's systematic philosophy of culture. By showing that mathematics has a paradigmatic character for Cassirer's entire philosophy of culture, insofar as it can be understood as a form of metasymbolic knowledge, an aspect of Cassirer's thinking that has received too little attention so far is revealed. Secondly, in the sense of a complementary completion, the project conference Ernst Cassirer's Theoretical Philosophy - Perspectives from the Philosophy of Mathematics and the Philosophy of Culture brought two previously largely independent strands of research into conversation with each other. It was explored how, on the one hand, Cassirer research in the philosophy of culture can benefit from a deeper insight into Cassirer's philosophy of mathematics. And how, on the other hand, the cultural-philosophical approach enables a 'deepening of the foundations' for Cassirer's philosophy of mathematics. To this end, researchers from both strands of research were brought together. In order to facilitate an exchange between the two groups, which until now have had little visibility for each other, but are nevertheless equally important for a more comprehensive interpretation of Cassirer. As a framework for the most productive dialogue possible, the organizers invited the speakers to illuminate central concepts of Cassirer's philosophy from their respective perspectives to enter into discussion with each other. The results of this productive conference, which was characterized by a lively exchange, will soon be published under the same title by Meiner Verlag in the Cassirer-Forschungen series.
Publications
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7 Geist und Zahl (De mente c. 6). Nicolaus Cusanus: Der Laie über den Geist / Idiota de mente, 107-130. De Gruyter.
Nickel, Gregor
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„Der Raum als Reihenbegriff – Ernst Cassirers Deutung der Geometrieentwicklung des 19. Jahrhunderts“. In: Siegener Beiträge zur Philosophie und Geschichte der Mathematik 16 (2022). Siegen: Universi, 175–198
Koenig, Daniel
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1. Mathematik und Sprache. Handbuch Sprache in Mathematik, Naturwissenschaften und Technik, 9-54. De Gruyter.
Nickel, Gregor
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Die Zahl als Denktypus. Zahlworte und Zahlbegriffe in der Symbolphilosophie Ernst Cassirers. Mathematik und mathematisches Denken – Ansprüche und Anforderungen vor, in und nach der Schule, 97-122. WTM Verlag.
Koenig, Daniel
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From Magnitudes to Real Numbers. Cantor's and Dedekind's Number Extensions and their Reception in the Marburg School of Neo-Kantianism 1. New Perspectives on Neo-Kantianism and the Sciences, 58-76. Routledge.
Koenig, Daniel
