Kant ’ s Transcendental Synthesis of the Imagination and Constructive Euclidean Geometry

ILLC MSc in Logic Riccardo Pinosio Friedman [1, 2] claims that Kant's constructive approach to geometry was developed as a means to circumvent the limitations of his logic, which has been widely regarded by various commentators as nothing more than a glossa to Aristotelian subject-predicate logic. Contra Friedman, and building on the work of Achourioti and van Lambalgen [3], we purport to show that Kant's constructivism draws its independent motivation from his general theory of cognition. We thus propose an exegesis of the Transcendental Deduction according to which the consciousness of space as a formal intuition of outer sense (with its properties of, e.g., infinity and continuity) is produced by means of the activity of the transcendental synthesis of the imagination in the construction of geometrical concepts, which synthesis must be in thoroughgoing agreement with the categories. In order to substantiate these claims, we provide an analysis of Kant's characterization of geometrical inferences and of geometrical continuity, along with a formal argument illustrating how the representation of space as a continuum can be constructed from Kantian principles.

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