Logic & Philosophy of Science Colloquium


Jeremy Heis
  University of Pittsburgh

"Abstracting Concepts and Constructing Concepts:  Concept Formation and Geometrical Construction in Kant and His Successors"


Some important recent work by Kant commentators has focused on Kant's theory of concept formation and its relation to the traditional theory of concept formation by abstraction.  I show that this seemingly narrow issue in Kant interpretation was a significant issue a century ago, when Kantian philosophers in Germany were developing new theories of concept formation as part of a wider project of understanding and justifying the methods of the sciences.  Specifically, these Kantian philosophers believed that they found a tension within Kant between the theory of concept formation by abstraction and the more promising idea that mathematicians construct mathematical objects from arbitrary concepts.  By downplaying the apparent abstractionism in Kant and generalizing Kant's theory of mathematical construction, they provided a philosophical justification for the conceptual innovations of more modern geometry and gave an interesting picture of mathematical existence, of the meaningfulness and syntheticity of mathematical judgments, and of the content of mathematical concepts and axioms.

Friday, January, 12, 2007
SST 777
3 pm

Refreshments will be served