Bertrand Russell’s Logicism versus Immanuel Kant’s Antinomies of Reason

Abstract

The article argues that the logicism through which Russell approached Kant’s antinomies possessed a distinct character, determined by: a) discovery of paradoxes, and b) theory of types as finding ways to solve them. The paper demonstrates both the strengths and weaknesses of Russell’s logicism regarding his approach to Kant’s mathematical antinomies, which concern the concepts of the world as a totality of phenomena and nature as a dynamic whole. The strengths of this logicism lie in the precise definitions of infinity and continuity as concepts of «pure arithmetic». Conversely, its weakness is the disregard for Kantian transcendentalism, the very framework within which the antinomies retain their meaning. It is transcendentalism as presupposing the subjective forms of intuition, space and time that renders the antinomies possible as productive ideas of reason. Rejecting these forms eliminates the «semantic field» within which the antinomies maintain their epistemological value.