Whereas the distinction between quantum properties and quantum states in the sense of pre-probabilities is often evident from the context and the use of different symbols, the case of a “pure state” in which the density operator can be written as a rank one projector or dyad, \(\rho =\dya{\psi}\), can lead to confusion in that the same mathematical object can represent either a pre-probability or a property. Indeed, there is a close connection in that if for such a \(\rho\) one introduces a sample space \(\{[\psi],I-]\psi]\}\), the probability of the property \([\psi]\) is 1, which is to say that if one uses this particular sample space the quantum system certainly has the property \([\psi]\). But if this same \(\rho\) is used as a pre-probability for some other sample space, and if one ignores the single framework rule, it is easy to fall into the trap of thinking that \([\psi]\) and some other incompatible property corresponding to a projector that does not commute with \([\psi]\) can both be true, which makes no sense. The best known example of the confusion that results is Schrödinger’s infamous dead-and-alive cat, subsection 10.1.