Published online by Cambridge University Press: 23 April 2021
While much attention has been paid to Kant’s, Fichte’s, Hegel's and even Maimon's philosophies of mathematics, little to no attention to has been given to the function (and importance) of mathematics in the work of Schelling. In the following, I argue that Schelling's flirtations with geometry, in conjunction with his utilisation of K. A. Eschenmayer's notion of Potenz as algebraic exponential, speak to an early form of intuitionist mathematics which is important to Schelling's thought in (at least) two areas: first, in discussing the relation of quantity to quality, and second, in constructing and describing thought as a species of motion. These pursuits, in diff erent but related ways, illustrate the complex form that Schelling uses to integrate human thought into nature, naturalising that which seems most artificial: the synthetic creations of mathematical intuition.
Furthermore, by focusing on the quantity–quality relation, one can demonstrate Schelling's diff erence from Fichte and the later Kant, while also pointing out Schelling's importance for contemporary thought and, subsequently, for the renewed significance of Naturphilosophie. Schelling's Identity philosophy, which concerns the mathematical through its focus on the logical form so important to Fichte (A = A), expands one concept from his Naturphilosophie, namely how the addition of quantities and qualities is to be understood and, subsequently, how this artithmetic connects to the deeper issue of the continuity of nature vis-à-vis the continuity of thought.
Schelling's Identity philosophy, which is often considered only slightly less of a dead dog than his Naturphilosophie, is commonly viewed as nestled in the shadow of Fichte's influence while simultaneously attempting to break free from it. In Schelling's Presentation of My System (1801) and Further Presentations of My System (1802), the themes of both motion and quantity/quality are evident, as Schelling writes in a Spinozistic (but also Fichtean) style (one of geometrical proofs, lemmas, postulates), while pushing beyond the strict activity of the I. Yet to regard these writings as simply amateurish, or as attempting to keep up with Fichte's demonstrable mathematical prowess, does a great disservice to Schelling's thought even at a relatively early stage.
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