Kant's Transcendental Synthesis of the Imagination and Constructive Euclidean Geometry
Riccardo Pinosio
Abstract:
Friedman 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, 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.