The literature contains a number of examples of a modal claim that can be made with possible worlds language but not in box-diamond language. Here is one that occurred to me that is simpler than any of the examples I’ve seen:
- Reality could have been different.
Very simple in possible worlds language: There is a non-actual world. (Note: This doesn’t work on the version of Lewis’s modal realism that allows for duplicate worlds. All the worse for that version.) But no box-diamond statement expresses (*). One can, of course, say that there aren’t any unicorns but could be, which implies (*), but that’s not the same as saying (*).