Soft axiomatisation
John von Neumann on method and von Neumann's method in the physical sciences
pp. 235-249
in: Emily Carson, Renate Huber (eds), Intuition and the axiomatic method, Berlin, Springer, 2006Abstract
Mathematical precision and rigour without conceptual clarity was for von Neumann neither possible nor desirable either in physical sciences or in mathematics. It seems justified to say that what drove von Neumann in his research, especially in physics, was the desire to achieve conceptual clarity and formulate conceptually consistent theories. Von Neumann's work on quantum mechanics and especially his abandoning the Hilbert space formalism corroborates this interpretation to a large extent. In arriving at acceptable theories von Neumann was relying on the method of an opportunistically interpreted soft axiomatics, a method of axiomatisation which was not affected by Gödel's results. Von Neumann himself, when speaking of the method in physics, emphasized that the aim of theoretical physics is to create mathematical models. His success in creating powerful mathematical models in physics was due to his unparalleled skill and talent in combining algebraic-combinatorial techniques with analysis.