 Third, the emergence of our classical world is not merely a matter of environmental decoherence (e.g., Omnés 1994; Berry 2001; Wallace 2012). For one thing, there is no context-free limit of infinitely many degrees of freedom because this limit always has uncountably infinitely many physically inequivalent representations. Moreover, it is simply false that an improper mixture of quantum states “allows one to interpret the state of the [quantum] system in terms of a classical probability distribution,” such that “it is useful to regard ‘mixed states’ as effectively classical,” so that “one can interpret the system described by [a nonpure density operator] in terms of a classical ‘mixture’ with the exact state of the system unknown to the observer” (Zurek 1991, 46–47). Impure quantum states can be interpreted as classical mixtures if and only if their components are described by disjoint states. For a classical mixture of two pure states (e.g., water and oil), the pure states are disjoint if and only if there exists a classical observable such that the expectation values with respect to these states are different. It is this disjointness that makes it possible to distinguish states in a classical manner. 