University of Pittsburgh

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

**Abstract:**

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.

SST 777

3 pm

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