Introduction

This chapter shows that Immanuel Kant's philosophy of mathematics sheds light on the doctrine that there are several stems of the cognitive capacity, which are distinct, but equally necessary for cognition. It explores the distinctive structure of outer sensible intuitions that must be understood in terms of the concept of magnitude and focuses on the act of sensibly representing a magnitude which involves a special act of spontaneity Kant ascribes to a capacity he calls the productive imagination. The chapter suggests what assumed by many commentators, it is not the case that the Two Stems Doctrine implies that a representation is either sensible or spontaneity-dependent, but not both. It discusses outer sensible intuitions are both sensible and spontaneity-dependent–they are sensible because they exhibit the kind of structure Kant takes to be distinctive of outer sensible intuitions, and they depend on spontaneity because they are cases of sensibly representing a magnitude.