Kant on Outer and Inner Intuition

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According to Kant, the primary propositions of geometry and arithmetic express synthetic apriori judgments. Though necessary, such judgments, being synthetic, must have a basis-a very special basis-in experience. Kant's theory of sensibility was his attempt to exhibit this special basis and thereby safeguard his characterization of the basis truths of mathematics. His theory's primary theses include the following: Sensibility, in contrast to understanding, is the capacity to have intuitions. Intuitions are either sensory (outer) intuitions or introspective (inner) intuitions. The former are representations of extended objects standing in spatial relationships; the latter are representations of temporal sequences of states of mind such as experiences, thoughts and feelings.' Space is the form of outer intuition; time is the form of inner intuition. Kant also asserted that neither the objects nor the forms of any intuitions have transcendental reality; they merely have phenomenal (empirical) reality.2 However, although neither outer nor inner intuition is apprehension of independent (transcendental) reality, both are related to bodies of synthetic apriori knowledge. Geometry Kant straightforwardly associated with outer intuition. In contrast, nowhere in the Transcendental Aesthetic, indeed nowhere in the Critique of Pure Reason, did Kant shed much light on the basis of arithmetic or the nature of the truths associated with inner intuition.3 In fact, considering its importance for his theory of