The Determinate World: Kant and Helmholtz on the Physical Meaning of Geometry

This study examines the place of Hermann von Helmholtz’s seminal papers on geometry in his philosophy of science. The arguments of these papers are traced back to his prior work on the theory of magnitudes, as well as to Helmholtz’s early, Kantian position. The author claims that Helmholtz should be understood not as opposing Kant, but as modifying the latter’s theory of magnitudes so as to remove obstacles to their common project of constructing a complete system of natural science.