Logic & Philosophy of Science Colloquium

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.