Main argument for a posteriori necessity uses these premises:
(P1) 'Hesperus' is a proper name that refers to the evening star. 'Phosphorus' is also a proper name and it refers to the morning star. But the evening star and the morning star are the same planetary body (Venus). So both names designate Venus.
(P2) If both names designate rigidly, they designate the same object (Venus) in every possible world. Therefore (by the definition of 'necessary') 'Hesperus = Phosphorus' is necessarily true. If it is the case that in all possible worlds the identity claim “Hesperus is Phosphorus” is true, the statement is necessary.
'Hesperus' and 'Phosphorus; are proper names that we give to the evening and morning stars in all possible worlds.There are a number of problems I see with this argument; for example:
1) The object (an eveing star/morning star) might not even exist in some possible world.
2) It is possible to have an evening as well as morning star but they could be different. It is only true in our world that evening and morning stars turned out to be the same planet. It doesn't follow they would be same in all possible worlds.
What is going on here?