 The decision to accept measurements and their outcomes as primitive concepts in our description of physical systems does not mean that we must forgo talk of the physical properties of such a system. Indeed, such talk is readily accommodated in the present formalism.[13]  In the approach we have been pursuing, a physical system is represented by a probabilistic model \((\mathcal{A},\Delta)\), and the system’s states are identified with the probability weights in \(\Delta\). Classically, any subset \(\Gamma\) of the state-space \(\Delta\) corresponds to a categorical property of the system. However, in quantum mechanics, and indeed even classically, not every such property will be testable (or “physical”). In quantum mechanics, only subsets of the state-space corresponding to closed subspaces of the Hilbert space are testable; in classical mechanics, one usually takes only, e.g., Borel sets to correspond to testable properties: the difference is that the testable properties in the latter case happen still to form a Boolean algebra of sets, where in the former case, they do not.