 The interpretation of projection operators as representing the properties of a physical system is already explicit in von Neumann’s Grundlagen.. However, the logical operations discussed there apply only to commuting projections, which are identified with simultaneously decidable propositions. In 1936 Birkhoff and von Neumann took a step further, proposing to interpret the lattice-theoretic meet and join of projections as their conjunction and disjunction, whether or not they commute. Immediately this proposal faces the problem that the lattice \(L(\mathbf{H})\) is not distributive, making it impossible to give these “quantum” connectives a truth-functional interpretation. Undaunted, von Neumann and Birkhoff suggested that the empirical success of quantum mechanics as a framework for physics casts into doubt the universal validity of the distributive laws of propositional logic. Their phrasing remains cautious: