Hegel’s (Anticipated) Answer to Peirce’s Stalled Critique of Cantor’s Analytic Continuum

Although Hegel is generally not known as a philosopher of mathematics, he maintained a deep interest in the history of mathematics, especially in its transformations between antiquity and the modern age. Charles S. Peirce, who was the son of a distinguished mathematician and was involved in developments in mathematics in the second half of the nineteenth century, was critical of what he perceived as Hegel’s lack of mathematical acumen. Nevertheless, he recognized in Hegel’s Science of Logic structural features of his own mathematically informed philosophy. In this article, I look to Hegel’s discussion of magnitude in The Science of Logic, and especially to his conception of the relation between continuous and discrete magnitudes, in order to articulate a solution he might have offered to difficulties encountered by Peirce in his opposition to Cantor’s set-theoretical analysis of the continuum. It is argued that Hegel’s interest in the ancient Platonic/Pythagorean tradition in mathematics provided him with crucial resources in this regard.