Michael Friedman
Dept. of Philosophy, University of Indiana, Bloomington, Indiana 47405
friedman@tarski.phil.indiana.edu

Title: Geometry, Construction, and Intuition in Kant and his Successors

The logical interpretation of Kant's theory of the role of intuition in
geoemtry originally articulated by Evert Beth and Jaakko Hintikka
conceives this role as primarily formal or inferential.  Intuition serves
to generate singlular terms in mathematical reasoning in inferences such
as we would represent today by existential instantiation.  On the approach
defended by Charles Parsons, by contrast, the primary role of intuition is
to acquaint us with certain phenomenological or perceptual spatial facts
which can then be taken to provide evidence for or to verify the axioms of
geometry. In this paper I try to build a bridge between the logical and
phenomenological interpretations by developing an account of what Kant
might mean by the a priori structure of perceptual space.  This a priori
structure is constituted by the subject's ability imaginatively to locate
itself in space at a particular point of view and with a particular
orientation or perspective, and then to change this point of view and
orientation by translation and rotation respectively. This interpretation
then allows us to connect Kant's doctrine with Hermann von Helmholtz's
work on space perception and the foundations of geometry, as well as with
the closely related work of Henri Poincare.  I conclude with a few remarks
on Hermann Weyl's generalized solution to the "space-problem," which, in a
certain sense, completes the story about space as a form of intuition
begun by Kant.