In propositional modal logic you can't express the distinction between "de dicto" modal statements and "de re" modal statements. Does this mean that all modal statements in propositional modal logic should be considered as being "de dicto"?
The difference between a "de re" and a "de dicto" statement concerns the place of the modal operator in a sentence and can be illustrated by means of the following example (which I borrow from a post by Fabio Somenzi):
◻∀x¬Cxx: It is necessarily true that nothing is the cause of itself (de dicto, the claim is necessarily true; i.e., the operator takes the whole sentence as its scope)
∀x◻¬Cxx: All things have the essential property of not being the cause of themselves (de re, all things have a necessary property; i.e., the modal property is ascribed to an object, not a sentence)
So my question is: given that in propositional modal logic you cannot express the difference between the two statements above (both "collapse" to ◻p) does this mean that every statement in modal propositional logic has to be considered as a "de dicto" statement? Or this question just doesn't make any sense?