When von Neumann codified the mathematical foundations of quantum mechanics in 1935, he also gave it an interpretation. Undoubtedly, he took that interpretation to be implicit in scientific practice. If there is such a thing as the mainstream understanding of the theory during the fifty years that followed this work, it is von Neumann's. As I shall try to show, it involved two principles, one tacit and one explicit. The first is that all quantum-mechanical description can be given in terms of state-attributions; the second his famous Projection Postulate, the 'acausal' state transition in measurement. Our first task will be to enquire how the two principles are related to each other, and whether they are forced on us by the theory.
The interpretation of quantum mechanics is a lively philosophical issue, and controversial. Stances on this issue included Einstein's realism, Bohr's and Heisenberg's versions of the Copenhagen interpretation, von Neumann's postulate of 'acausal' collapse of the wave function, and the 'ensemble' interpretation of states. These views did not constitute specific, rigorously developed interpretations, such as we now have (notably, those which emerged in the detailed foundational work of Mittelstaedt, and of Ludwig; the quantum-logical interpretation developed by Putnam, Bub, Demopoulis, Friedman, and Stairs; the 'operational' theory of theories due to Foulis and Randall; the 'perspectival' interpretation of Kochen; and the 'modal' interpretation which I shall elaborate below). To understand such answers, we need to understand the question. So we must first ask: what is an interpretation of a theory? And this question in turn must be preceded by: what is a theory?