The challenge of bad infinity: A restatement of Hegel’s critique of mathematics

Hegel’s critique of mathematics cannot be reduced to mathematics alone. At least this is the stake of the present paper: to argue that a comprehensive understanding of the matter cannot be confined strictly to the philosophy of science. Indeed, Hegel’s philosophy of mathematics pervades his entire ontology and, within the system, his political philosophy. Starting with Hegel’s logic, the article advances towards the fact that Hegel did not reject mathematics in itself, nor he denied the incalculable merits of exact sciences made possible by applied mathematics. What he considered risky regarding mathematics was its revindication of the explanation of movement to the disadvantage of philosophy. Hence, the possibility of a technocratic world incapable of seeing and going beyond itself.