 The problems mentioned above do not arise for type-I\(_n\) factors, if \(n\lt \infty\), nor do they arise for type-II\(_1\). That is to say, these factor types have a finite trace operation and are not plagued with the domain problems of unbounded operators. Particularly noteworthy is that the lattice of projections of each of these factor types (type-I\(_n\) for \(n\lt \infty\) and type-II\(_1)\) is modular. By contrast, the set of bounded operators on an infinite-dimensional separable Hilbert space, a type-I\(_{\infty}\) factor, is not modular; rather, it is only orthomodular. These considerations serve to explain why von Neumann regarded the type-II\(_1\) factor as the proper generalization of the type-I\(_n\) \((n\lt \infty)\) for quantum physics rather than the type-I\(_{\infty}\) factors. The shift in the literature from modular to orthomodular lattices that was characterized above is in effect a shift back to von Neumann’s earlier position (prior to his confession). But, as was already mentioned, it now seems that this was not the best move either.