Some notes from Jay Richards’ Untamed God.
The definition of essence is a set of properties that an entity exemplifies (64). A property is some fact or truth about an entity in the world. In our usage we want to say that Socrates has necessary/essential properties without saying that Socrates is necessary to every possible world. We would say it like this:
“S has P and there is no W in which S has the complement ~P of P.
Property actualism states that S has no properties in worlds in which he does not exist.
□(x)(P(x) → E(x))
Therefore, The essentialist argues that there is a distinction between essential divine properties and accidental (contingent) divine properties (90). Property: a state of affairs concerning entities of different types. While saying there are contingent properties in God seems to depart from the tradition, it really doesn’t. God’s deciding to create the world is a contingent divine property. God has P in every world. God’s essence is concretely instantiated in every possible world (95). God’s essential attributes, those he has in every possible world, are divine ‘perfections’ (96). “They include all those properties susceptible to perfection.”
Scholastic Tory 