Abstract:
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.
Michael Stöltzner
"Action Principles and Teleology." In Harald Atmanspacher and Gerhard J. Dalenoort, eds., Inside versus Outside: Endo- and Exo-concepts of Observation and Knowledge in Physics, Philosophy, and Cognitive Science, pp. 33-62. Springer Series in Synergetics, 63. Berlin & New York: Springer-Verlag, 1994.
(with Walter Thirring.) "Entstehen neuer Gesetze in der Evolution der Welt." Naturwissenschaften (June 1994), 81(6):243-249.
"Levels of Physical Theories." In Werner DePauli-Schimanovich, Eckehart Köhler, and Friedrich Stadler, eds., The Foundational Debate, pp. 47-64. Vienna Circle Institute Yearbook, 3. Dordrecht & Boston: Kluwer, 1995.
"Philipp Frank and the German Physical Society."
In Werner DePauli-Schimanovich, Eckehart Köhler,
and Friedrich Stadler, eds.,
The Foundational Debate, pp. 293-302. Vienna Circle Institute
Yearbook, 3.
Dordrecht & Boston: Kluwer, 1995.
"Contains in the main the proceedings of the conference 'The
Foundational Debate: Constructivity and Complexity in Logic, Mathematics and Physics',
held at the Mathematical Institute of the University of Vienna in September, 1994,
organized by the Institute Vienna Circle"--p. ix.
Review of Julian B. Barbour's Mach's Principle: From Newton's Bucket to Quantum Gravity. In Werner DePauli-Schimanovich, Eckehart Köhler, and Friedrich Stadler, eds., The Foundational Debate, pp. 313-315. Vienna Circle Institute Yearbook, 3. Dordrecht & Boston: Kluwer, 1995.
"Vienna-Berlin-Prague: Centenaries Carnap, Reichenbach, Zilsel." In Werner DePauli-Schimanovich, Eckehart Köhler, Friedrich Stadler, eds., The Foundational Debate, pp. 317-342. Vienna Circle Institute Yearbook, 3. Dordrecht & Boston: Kluwer, 1995.
"The Auxiliary Motive in the Forest and in Optics." In Elisabeth Nemeth and Friedrich Stadler, eds., Encyclopedia and Utopia: The Life and Work of Otto Neurath (1882-1945), pp. 113-126. With the first publication of Otto Neurath's full manuscript on 'Visual Education' and the documentation of the "Otto Neurath Nachlasss" (Haarlem, The Netherlands). Vienna Circle Institute Yearbook, 4. Dordrecht & Boston: Kluwer, 1996.
"Gödel and the Theory of Everything." In Petr Hájek, ed., Gödel '96: Logical Foundations of Mathematics, Computer Science, and Physics--Kurt Gödel's Legacy, pp. 291-306. Brno Czech Republic, August 1996, Proceedings. Lecture Notes in Logic, 6. Berlin & New York: Springer, 1996.
"Quantenmechanik und Schulphilosophie." In Alfred Schramm, ed., Philosophie in Österreich 1996: Vorträge des IV. Kongresses der Österreichischen Gesellschaft für Philosophie, Graz, 28. Februar-2. März 1996, pp. 132-136. Vienna: Hölder-Pichler-Tempsky, 1996.
Review of Bernard d'Espagnat's Veiled Reality: An Analysis of Present-Day Quantum Mechanical Concepts. In Elisabeth Nemeth and Friedrich Stadler, eds., Encyclopedia and Utopia: The Life and Work of Otto Neurath (1882-1945), pp. 385-389. Vienna Circle Institute Yearbook, 4. Dordrecht & Boston: Kluwer, 1996.
"Formale Intuition jenseits und diesseits der Kunst." In Peter Weibel, ed.,
Jenseits von Kunst, pp. 18-21. Vienna: Passagen-Verlag, 1997.
Catalog of an exhibition held at the
Ludwig Museum Budapest
Oct. 17-Nov. 23, 1996 and at the Neue Galerie am Landesmuseum
Joanneum Graz Feb. 7-Mar. 30, 1997.
Review of Paolo Parrini's Conoscenza e realità: saggi di filosofia positiva. In Werner Leinfellner and Eckehart Köhler, eds., Game Theory, Experience, Rationality: Foundations of Social Sciences, Economics and Ethics: In Honor of John C. Harsanyi, pp. 415-420. Vienna Circle Institute Yearbook, 5. Dordrecht & Boston: Kluwer, 1998.
"Commento a Massimo Ferrari." In Michele Di Francesco, Diego Marconi, and Paolo Parrini, eds., Filosofia analitica, 1996-1998: prospettive teoriche e revisioni, pp. 49-57. Milan: Guerini studio, 1998.
"Federico Enriques e l'Enciclopedia neurathiana." Rivista di Storia della Filosofia (1998), 53(3):463-494.
"Neurath's Auxiliary Motive as the Limit Case of Inductive Reasoning." In Paul Weingartner, Gerhard Schurz, and Georg Dorn, eds., The Role of Pragmatics in Contemporary Philosophy: Papers of the 20th International Wittgenstein Symposium, August 10-16, 1997, Kirchberg am Wechsel/Die Rolle der Pragmatik in der Gegenwartsphilosophie: Beiträge des 20. Internationalen Wittgenstein Symposiums: 10.-16. August, 1997, Kirchberg am Wechsel , pp. 933-938. Schriftenreihe der Wittgenstein-Gesellschaft, Bd. 26. Vienna: Hölder-Pichler-Tempsky, 1998.
"Probability, Dynamics and Causality." Review of Domenico Costantini and Maria Carla Galavotti, eds., Probability, Dynamics and Causality. Nuncius (1998), A13(2):751-755.
"Gödels Theoreme als Brücke zwischen Mathematik und Physik." In Winfried Löffler and Edmund Runggaldier, eds., Vielfalt und Konvergenz der Philosophie: Innsbruck, 1.-4. Februar 1998 pp. 186-191. Vorträge des V. Kongresses der Österreichischen Gesellschaft für Philosophie. Teil 1. Schriftenreihe der Österreichischen Gesellschaft für Philosophie, 2. Vienna: Hölder-Pichler-Tempsky, 1999.
"On Various Realisms in Quantum Theory." In Maria Carla Galavotti and Alessandro Pagnini, eds., Experience, Reality, and Scientific Explanation: Essays in Honor of Merrilee and Wesley Salmon, pp. 163-186. The Western Ontario Series in Philosophy of Science, 61. Dordrecht & Boston: Kluwer Academic, 1999.
"To What Extent Does Formal Teleology Still Make Sense." In Marta Féhér, Olga Kiss, and Laszlo Ropolyi, eds., Hermeneutics and Science: Proceedings of the First Conference of the International Society for Hermeneutics and Science, pp. 227-246. Boston Studies in the Philosophy of Science, 206. Dordrecht & Boston: Kluwer, 1999.
"Über zwei Formen von Realismus in der Quantentheorie." Journal for General Philosophy of Science/Zeitschrift für Allgemeine Wissenschaftstheorie (1999), 30:271-298.
"Vienna Indeterminism: Mach, Boltzmann, Exner." Synthese (1999), 119(1-2):85-111.
"What John von Neumann Thought of the Bohm Interpretation." In Daniel Greenberger, Wolfgang L. Reiter, and Anton Zeilinger, eds., Epistemological and Experimental Perspectives on Quantum Physics, pp. 257-262. Vienna Circle Institute Yearbook 7. Dordrecht & Boston: Kluwer, 1999.
"Zeroth Order Teleology: The Principle of the Distinguished Case." In Uwe Meixner and Peter Simons, eds., Metaphysics in the Post-Metaphysical Age: Papers of the 22nd International Wittgenstein Symposium, August 15-21, 1999, Kirchberg am Wechsel = Metaphysik im postmetaphysischen Zeitalter: Beiträge des 22. internationalen Wittgenstein Symposiums, 15.-21. August 1999, Bd. 2. Vol. 2, pp. 284-290. Kirchberg am Wechsel. Contributions of the Austrian Ludwig Wittgenstein Society, 7. Kirchberg am Wechsel: Austrian Ludwig Wittgenstein Society, 1999.
(with Walter Thirring.) "Entstehen neuer Gesetze in der Evolution der Welt." In Ludwig Huber, ed.,Wie das Neue in die Welt kommt: Phasenübergänge in Natur und Kultur, pp. 57-70. Vienna: WUV, 2000.
"La filosofia italiana e la filosofia austriaca." In Atti del Convegno Società Filosofica Italiana Verso il 2000. Milan: Mondadori, 2000.
"A Physicist's Comment to Rosenberg." In Martin Carrier, Gerald J. Massey, and Laura Ruetsche, eds., Science at Century's End: Philosophical Questions on the Progress and Limits of Science, pp. 265-283. Pittsburgh-Konstanz Series in the Philosophy and History of Science. Pittsburgh, Pa.: University of Pittsburgh Press, 2000.
"Das Prinzip der kleinsten Wirkung." In Barbara Boisits and Sonja Rinofner-Kreidl, eds., Organologische Denkmodelle in der Moderne, pp. 341-381. Studien zur Moderne 11. Vienna: Passagen-Verlag, 2000.
Review of Elisabeth Nemeth, Richard Heinrich, and Antonia Soulez, eds., Otto Neurath: Rationalität, Planung, Vielfalt. Die Presse - Spekrum (March 18/19 2000).
"Zur Gegenstandskonstitution in der Ästhetik Bolzanos." In M. Seiler and F. Stadler, eds., Kunst, Kunsttheorie und Kunstforschung im wissenschaftlichen Diskurs. In memoriam Kurt Blaukopf (1914-1999), pp. 227-248. Vienna: ÖBV-HPT, 2000.
Edited (with G. Kampis and L. Kvasz.) Appraising Lakatos. Mathematics, Methodology, and the Man. Dordrecht & Boston: Kluwer, 2001.
Edited (with M. Rédei.) John von Neumann and the Foundations of Quantum Physics. Vienna Circle Yearbook, 8. Dordrecht & Boston: Kluwer, 2001.
"Opportunistic Axiomatics: John von Neumann on the Methodology of Mathematical Physics." In Michael Stöltzner and M. Rédei, eds., John von Neumann and the Foundations of Quantum Physics, pp. 35-62. Vienna Circle Institute Yearbook 8. Dordrecht & Boston: Kluwer, 2001.
"Vienna Indeterminism II: From Exner to Frank and von Mises." In Paolo Parrini, Wesley Salmon, and P. Murray, eds., The Origins of Logical Empiricism: Analytical and Continental Perspectives. Pittsburgh: University of Pittsburgh Press, 2001.
(with B. Buldt, E. Köhler, W. Schimanovich, C. Klein and P. Weibel.) Wahrheit und Beweisbarkeit.
"What Lakatos Could Teach the Mathematical Physicist." In G. Kampis, L. Kvasz, and Michael Stöltzner, eds., Appraising Lakatos: Mathematics, Methodology, and the Man. Dordrecht & Boston: Kluwer, 2001.
"The Least Action Principle as the Empiricist's Shibboleth." In Proceedings of HOPOS 2000.