VON NEUMANN, EMPIRICISM AND THE FOUNDATIONS OF QUANTUM MECHANICS

摘要

1. Introduction The issue of the application of mathematics to natural science has received a great deal of consideration in the last few years (see, for instance, Field [1980] and [1989], Hellman [1989], Steiner [1989] and [1998], and Shapiro [1997]). In this paper, I am concerned with two tasks: (1) to provide a formal framework to accommodate one important aspect of this issue --the heuristic use of mathematics in theory construction -- and (2) to illustrate how this framework works by focusing on a particular case-study: von Neumann's use of logic and set theory in his work in the foundations of quantum mechanics. The reason to consider von Neumann's work derives from the interplay of mathematical, logical and heuristic considerations that he wove together in the process of providing an axiomatization for quantum mechanics and exploring some of its consequences. Moreover, his work provides important insights into the nature of theory construction in physics.