Las determinaciones matemáticas del tiempo y el espacio

la reformulación de Paul Natorp del idealismo crítico de Kant

Abstract

This paper analyzes Paul Natorp's reformulation of the Kantian conception of space and time. In the Transcendental Aesthetic, Kant argues that space and time are forms of sensibility, irreducible to the functions of the understanding, and that their fundamental properties, unity, infinity, homogeneity, and continuity, follow directly from their intuitive character. The Marburg School of Neo-Kantianism considers this distinction between faculties to be a limitation of Kantian idealism and proposes to overcome it. Within this framework, Natorp argues that space and time are not forms of sensibility but functions of thought, and that their mathematical properties are not given in intuition but derived from the laws of pure thinking. The paper reconstructs Natorp's position in four steps. First, it examines the properties of space and time in Kant's Transcendental Aesthetic. Second, it presents the reasons why Natorp considers it necessary to overcome the Kantian dualism of faculties, and reconstructs the synthesis of quantity and quality through which thought constitutes the object as magnitude. Third, it analyzes the level of relation, where thought produces space and time as specific functions of order. Fourth, it shows how the mathematical properties of space and time are derived from the fundamental series as expressions of the same operations of thought that generate number. It is argued that, for Natorp, number logically precedes space and time, thereby inverting the Kantian order of grounding. The case of the three-dimensionality of space is examined as the structural limit of this mathematical derivation.