 In all possible worlds, Socrates is such that there are infinitely many primes (whether Socrates is concrete or non-concrete). Thus, condition (2) is not satisfied. Thus, this is not one of Socrates’s essential properties. (In Zalta’s terminology, this is not one of Socrates’s strongly essential properties, although Zalta would say that it is one of Socrates’s weakly essential properties, since condition (1) is satisfied.) Here is Zalta’s account of essence for abstract objects: