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The Relevance of RomanticismEssays on German Romantic Philosophy$
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Dalia Nassar

Print publication date: 2014

Print ISBN-13: 9780199976201

Published to Oxford Scholarship Online: April 2014

DOI: 10.1093/acprof:oso/9780199976201.001.0001

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Friedrich Schlegel’s Romantic Calculus

Friedrich Schlegel’s Romantic Calculus

Reflections on the Mathematical Infinite around 1800

Chapter:
(p.239) 13 Friedrich Schlegel’s Romantic Calculus
Source:
The Relevance of Romanticism
Author(s):

John H. Smith

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199976201.003.0014

This chapter explores the way German thinkers in the decades around 1800 recognized that the new mathematics, especially differential calculus as it was developed by Leonard Euler, had important philosophical and aesthetic consequences. Novalis, Schlegel, Schleiermacher, Schelling, and Hegel all exploited in different ways the fundamental paradoxes inherent in thinking about infinity, continuity, and the infinitesimal. Although these mathematical concepts were powerfully effective in quantifying motion and change in physical reality, and were thus as concrete as the arc described by a flying object, they nonetheless defy representation. The thinkers discussed in this paper saw this paradoxical concrete unrepresentability of mathematics as itself a metaphor for ontological and creative processes. Their uses of this metaphor had effects beyond the period of romanticism.

Keywords:   infinite, mathematics, mathematical infinite, unrepresentability, Leonard Euler, Schlegel, romanticism, Hegel, Maimon, Kant

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