| Summary: | Kant notoriously holds that mathematical knowledge is irreducibly (though not exclusively) sensible. But scholars have not appreciated a radical consequence of this view. For Kant also holds that humans can grasp the mathematically infinite; and he thinks we can do so not despite but precisely because of the fact that math is sensibly grounded. Since our senses are manifestly limited in scope and acuity, rationalists and empiricists alike have traditionally held that infinitary knowledge is possible only if it is not sensible. Kant's conception of sensibility is paradoxically meant to have its paradigmatic manifestation in perception yet also ground infinitary knowledge in mathematics. By understanding how this is possible, I argue, we can recover a philosophically fruitful notion of sensible representation and shed new light on Kant's cognitive-capacity approach to epistemology. Kant rejects both the rationalists' logical conception of sensibility (as confused representation) and the empiricists' phenomenological conception (as vivacity to consciousness). I defend a novel account of Kantian sensibility as resting on a functional analysis of our cognitive finitude: whatever outstrips our finite capacity for discursive thought must, ipso facto, be given to us (i.e. sensibly presented) if it is to be thought at all. This account explains the sensible status of perception as well as infinitary mathematics, since both provide the mind with contents whose complexity discursive thought can accommodate, but never originate. Moreover, this conception of human sensibility emerges out of a functional analysis of our self-understanding as finite knowers. This opens up the possibility of an a priori approach to the philosophy of mind that eschews the traditional, ontological view of the mind as a thinking substance.
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