 As mentioned above, realist interpretations of quantum mechanics must be careful in how they construe the phrase “the observable \(A\) has a value in the set \(B\)”. The simplest and most traditional proposal—often dubbed the “eigenstate-eigenvalue link” (Fine [1973])—is that (*) holds if and only if a measurement of \(A\) yields a value in the set \(B\) with certainty, i.e., with (quantum-mechanical!) probability 1. While this certainly gives a realist interpretation of  (*),[5]  it does not provide a solution to the measurement problem. Indeed, we can use it to give a sharp formulation of that problem: even though \(A\) is certain to yield a value in \(B\) when measured, unless the quantum state is an eigenstate of the measured observable \(A\), the system does not possess any categorical property corresponding to \(A\)’s having a specific value in the set \(B\). Putnam seems to assume that a realist interpretation of (*) should consist in assigning to \(A\) some unknown value within \(B\), for which quantum mechanics yields a non-trivial probability. However, an attempt to make such assignments simultaneously for all observables runs afoul of Gleason’s  Theorem.[6]