For any world w, Paul has the rigidified property of actually being on David's right in w just in case in the actual world Paul has the contingent property of being on David's right.
possible world (w)(in modal logic and metaphysics)
An imaginary, logically consistent scenario—a way things could have been instead of how they actually are; philosophers use it to talk about what's possible versus what's actual.
rigidified property(in metaphysics and logic)
A property that refers to something specific about the actual world, and keeps that same reference in all imaginary scenarios—like using a permanent label rather than a flexible description.
The second response involves moving from contingent properties like those involved in (2) and (3) to necessary properties, and in particular to what, following Plantinga in (1974), we will call an individual essence, which is a property that, necessarily, if x exists, then it has that property and, necessarily, only x has. The property being on David's right is not an individual essence of Paul, as Paul might have existed without having had it and Charles might have had it instead. But it is eas