  An abstraction mechanism will be used to disambiguate our syntax. The de re reading will be symbolized \([\lambda x\,\Diamond P(x)](f)\) and the de dicto will be symbolized \(\Diamond [\lambda x\,P(x)](f)\). The (incomplete) expression \([\lambda x\,X]\) is often called a predicate abstraction; one can think of it as the predicate abstracted from the formula \(X\). In \([\lambda x\,\Diamond P(x)](f)\) we are asserting that \(f\) has the possible-\(P\) property, while in \(\Diamond [\lambda x\,P(x)](f)\) we are asserting the possibility that \(f\) has the \(P\) property. Abstraction disambiguates. What we have said about \(\Diamond\) applies equally well to \(\Box\) of course. It should be noted that one could simply think of abstraction as a scope-specifying device, in a tradition that goes back to Russell, who made use of such a mechanism in his treatment of definite descriptions. Abstraction in modal logic goes back to Carnap 1947, but in a way that ignores the issues discussed above. The present usage comes from Stalnaker &amp; Thomason 1968 and Thomason &amp; Stalnaker 1968.