  Here’s an example to show how the semantics works in a technical way. An intension is rigid if it is constant, the same in every state. We might think of a rigid intension as a disguised object, identifying it with its constant value. It should not be a surprise, then, that for rigid intensions, the distinction between de re and de dicto disappears. Indeed, something a bit stronger can be shown. Instead of rigidity, consider the weaker notion called local rigidity in Fitting and Mendelsohn 1998: an intension is locally rigid at a state if it has the same designation at that state that it has at all accessible ones. To say \(f\) is locally rigid at a state, then, amounts to asserting the truth of \([\lambda x\,\Box [\lambda y\,x = y](f)](f)\) at that state. Local rigidity at a state implies the de re /de dicto distinction vanishes at that state. To show how the formal semantics works, here is a verification of the validity of