Friedrich Schlegel’s Romantic Calculus
Friedrich Schlegel’s Romantic Calculus
Reflections on the Mathematical Infinite around 1800
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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