Full Idea
Necessarily any necessary truth will hold if Socrates exists. But it is no part of Socrates' essence that there be infinitely many prime numbers, ..or that objects like the Eiffel Tower have their own necessary essence.
Gist of Idea
It is not part of the essence of Socrates that a huge array of necessary truths should hold
Source
Kit Fine (Essence and Modality [1994], p. 5-6)
Book Reference
-: 'Philosophical Perspectives' [-], p.5
A Reaction
This and the 'singleton Socrates' example (Idea 11165) are the twin prongs of Fine's attack on the modal account of essentialism. I think they constitute one of the best single pages in the whole of recent philosophy. Bravo.
Related Idea
Idea 11165 If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K]