# Logic & Philosophy of Science Colloquium

**Michael Stöltzner**

University of California, Irvine

Universität Salzburg

Institut Wiener kreis

## “Opportunistic Axiomatics

John von Neumann on the Methodology of Mathematical Physics
”

No other mathematician has shaped post-war
mathematical physics to a larger extent than John von Neumann. In
this talk I intend to show that his methodological remarks of the
1940s and 1950s also open up an interesting philosophical
perspective on the interaction between mathematics and physics
which can be conceived as a pragmatist re-interpretation of
Hilbert's program of the axiomatization of the empirical sciences.
On this basis, axiomatization can prove fertile both in physically
well-entrenched theories, such as quantum mechanics, and in cases
where the basic concepts of the science are not yet fully clarified
and empirical evidence is still poor, such as game theory. The main
reason is that mathematization and axiomatization permit great
flexibility and opportunism in concept formation and allow a
continuous application of pragmatic criteria of success from the
sciences to mathematics proper. In this way even some motives from
the foundational debates in mathematics appear in a pragmatist mode
without any absolutist ambitions. To make my point concerning the
timeliness of von Neumann's opportunistic axiomatics more precise,
I shall first investigate which stand he could take in the debates
on the character string theorists" "theoretical mathematics"
stirred up by Arthur Jaffe and Frank Quinn in 1993/4. Secondly, I
ask how von Neumann's opportunistic axiomatics is related to the
distinction between mathematical optimism and mathematical
opportunism recently drawn by Mark Wilson.

## Friday, April 6, 2001

SST 777

3 pm

*Refreshments will be served*

©