Lanier Anderson

	Contextualizing Kant's Philosophy of Mathematics


The most famous claim of Kant's philosophy of mathematics is that
mathematical cognition is not analytic, but synthetic, and that this
fact is shown by the role of "construction" in mathematical argument.
Much of the recent discussion of Kant's view can be organized around
two positions on the role of this construction: one side (Hintikka,
Friedman) attributes a *logical* role to construction, and the other
side (Parsons, et al.)  thinks it has a *phenomenological* role.  On
the logical reading, mathematical constructions like the diagrams of
Euclidean geometry play an ineliminable role in arguments for
particular theorems, whereas on the phenomenological reading,
constructions provide a kind of direct evidence in support of the
axioms of elementary mathematics.  I will discuss some recent advances
in our understanding of Kant that support a version of the logical
reading, but I will also argue that prominent recent versions of the
logical readings tend to overemphasize issues that seem prominent only
from a post 19th c. point of view, and underplay key aspects of the
role of diagrammatic constructions in the sort of arguments Euclid
himself gives.  These latter considerations are closer to what Kant
himself had in mind in attributing such importance to construction.
If there is time, I will point out some of the wider epistemological
consequences of this notion of construction in Kant's theory of
cognition.