Kant's account of space as an infinite given magnitude in the Critique of Pure Reason is paradoxical, since infinite magnitudes go beyond the limits of possible experience. Michael Friedman's and Charles Parsons's accounts make sense of geometrical construction, but I argue that they do not resolve the paradox. I argue that metaphysical space is based on the ability of the subject to generate distinctly oriented spatial magnitudes of invariant scalar quantity through translation or rotation. The set of determinately oriented, constructed geometrical spaces is a proper subset of metaphysical space, thus, metaphysical space is infinite. Kant's
paradoxical doctrine of metaphysical space is necessary to reconcile his
empiricism with his transcendental idealism.