Full Idea
A rigid designator is a designator that denotes the same individual in all possible worlds; doesn't this presuppose that the same individuals can be found in differing possible worlds?
Gist of Idea
Rigid designation seems to presuppose that differing worlds contain the same individuals
Source
Robert C. Stalnaker (Reference and Necessity [1997], 5)
Book Reference
Stalnaker,Robert C.: 'Ways a World Might Be' [OUP 2003], p.185
A Reaction
This is part of Stalnaker's claim that Kripke already has a metaphysics in place when he starts on his semantics and his theory of reference. Kripke needs a global domain, not a variable domain. Possibilities suggest variable domains to me.
Related Ideas
Idea 16394 Kripke derives accounts of reference and proper names from assumptions about worlds and essences [Stalnaker on Kripke]
Idea 16411 If possible worlds really differ, I can't be in more than one at a time [Stalnaker]