 As a result of his earlier work on the foundations of quantum mechanics and his work on quantum logic with Birkhoff, von Neumann came to regard the type-II\(_1\) factors as likely to be the most relevant for physics. This is a substantial shift since the most important class of algebra of observables for quantum mechanics was thought at the time to be the set of bounded operators on an infinite-dimensional separable Hilbert space, which is a type-I\(_{\infty}\) factor. A brief explanation for this shift is provided below. See the well-informed and lucid account presented in (Rédei 1998) for a much fuller discussion of von Neumann’s views on fundamental connections between quantum logic, rings of operators (particularly type-II\(_1\) factors), foundations of probability theory, and quantum physics. It is worth noting that von Neumann regarded the type-III factors as a catch-all class for the “pathological” operator algebras; indeed, it took several years after the classificatory scheme was introduced to demonstrate the existence of such factors. It is ironic that the predominant view now seems to be that the type-III factors are the most relevant class for physics (particularly for QFT and quantum statistical mechanics). This point is elaborated further in Section 4.1 after explaining below why von Neumann’s program never came to fruition.