4 - Extensive and Intensive Magnitudes and Continuity

Summary

Chapter 4 completes the new interpretation of the Axioms of Intuition by reconstructing the argument that all appearances and intuitions are not just magnitudes, but extensive magnitudes. It also examines the Anticipations of Perception, which concerns intensive magnitudes, and clarifies Kant’s distinction between extensive and intensive magnitude, which depends on their mereology. An infinite regress appears to threaten Kant’s mereological definition of extensive magnitude, since the representation of a whole extensive magnitude presupposes the representation of its parts, ad infinitum. The regress is avoided by the indeterminate representation of parts that are not themselves extensive magnitudes. There are several different accounts of how the parts of space can be indeterminately represented. The chapter examines and rejects two of them and argues for a third: they are indeterminately represented through a continuous successive synthesis of space in the generation of a representation of an extensive magnitude. This interpretation is supported by Kant’s explanation of continuity and he references to Newton’s theory of fluxions and fluents. The chapter concludes by arguing that the manifold of a continuous quantum can be indeterminately cognized under the category of plurality, while all three categories of quantity are required for the cognition of quantitas.