My objection to the modal accounts will be to the sufficiency of the proposed criterion, not to its
necessity. I accept that if an object essentially has a certain property then it is necessary that it has
the property (or has the property if it exists); but I reject the converse. For the time being, we shall
confine our attention to the existentially conditioned form of the criterion. Once the objection is
developed for this form, it will be clear how it is to be extended to the categorical form.
Consider, then, Socrates and the set whose sole member is Socrates. It is then necessary, according
to standard views within modal set theory, that Socrates belongs to singleton Socrates if he exists;
for, necessarily, the singleton exists if Socrates exists, and, necessarily, Socrates belongs to
singleton Socrates if both Socrates and the singlcton exist. It therefore follows according to the
modal criterion that Socrates essentially belongs to singleton Socrates.
But, intuitively, this is not so. It is no part of the essence of Socrates to belong to the singieton.
Strange as the literature on personal identity may be, it has never been suggested that in order to
understand the nature of the person one must know to which sets he belongs. There is nothing in
the nature of a person, if I may put it this way, which demands that he beiongs to this or that set or
which even demands that there be any sets.