Recent mathematical results, obtained by the author, in collaboration with Alexander Stokolos, Olof Svensson, and Tomasz Weiss, in the study of harmonic functions, have prompted the following reflections, intertwined with views on some turning points in the history of mathematics and accompanied by an interpretive key that could perhaps shed some light on other aspects of (the development of) mathematics.

In “Violence and Metaphysics” Jacques Derrida suggests that “the only effective position to take in order not to be enveloped by Hegel would seem to be…to consider false-infinity…irreducible.” Inversely, refuting the charge of logocentrism associated with Hegelian true infinity ( wahrhafte Unendlichkeit ) would involve showing that Hegel’s speculative logic does not establish the infinity of being exempt from the negativity of the finite. This paper takes up Derrida’s challenge, and argues that true infinity is crucial to Hegel’s understanding of (...) ideality as a question of normative authority, which does not fall prey to logocentrism. Through an exposition of the dialectic of the finite and the infinite in Hegel’s Science of Logic , I argue that true infinity is not an ontological category that eliminates division, but rather refers to the metalogical standpoint involved in a philosophical account of determinacy. Although fully achieved at the end of the Logic , the metalogical standpoint that Hegel elaborates in the Seinslogik under the banner of the true infinite already clarifies that determinacy is a product of normative authority that is itself precarious. (shrink)