Hilbert-style axiomatic completion: On von Neumann and hidden variables in quantum mechanics.

In this paper I provide a detailed history of von Neumann's "No Hidden Variables" theorem, and I argue it is a demonstration that his axiomatization mathematically captures a salient feature of the statistical transformation theory (namely, that hidden variables are incompatible). I show that this reading of von Neumann's theorem is obvious once one recalls several factors of his work. First, his axiomatization was what I call a Hilbert-style axiomatic completion; indeed, it developed from work initiated by Hilbert (and Nordheim).