# Logic & Philosophy of Science Colloquium

**Richard Zach**

University of California, Berkeley

## “The practice of finitism:

epsilon-calculus and consistency proofs in Hilbert's program”

David Hilbert's well-known program for the foundations of
mathematics presents a challenge for the history and philosophy of
mathematics: Like Frege's and Russell's logicist projects, here a
philosophical position is closely tied up with a mathematical
problem. Not only does the strength of the philosophical position
depend on a solution of the mathematical problem, but also, or so I
argue, the understanding and interpretation of the philosophical
position depends on an understanding of the methods used in
attacking the mathematical questions. In my talk, I investigate
two aspects of Hilbert's mathematical project; the formalization of
mathematics in the epsilon-Calculus and some attempted consistency
proofs for systems so axiomatized. I will show how a study of the
mathematical practice of the finitist program sheds light on the
two philosophical pillars of Hilbert's project: instrumentalism and
the strength of finitist reasoning.

## Friday, January 26, 2001

SST 777, 3 pm

*Refreshments will be served*

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