In Quantified modal logic, "constancy’s defenders can point to certain powerful arguments in its favor.
Here’s a quick sketch of one such argument. First, the following seems to be a logical truth:
Ted = Ted
But it follows from this that: ∃y y = Ted
This latter formula, too, is therefore a logical truth. But if φ is a logical truth then so is □φ (recall the rule of necessitation from chapter 6). So we may infer that the following is a logical truth:
□∃y y = Ted
Now, nothing in this argument depended on any special features of me. We may therefore conclude that the reasoning holds good for every object; and so ∀x□∃y y = x is indeed a logical truth. Since, therefore, every object exists necessarily, it should come as no surprise that there are things that might have been ghosts, dragons, and so on— for if there had been a ghost, it would have necessarily existed, and thus must actually exist.
This and other related arguements have apparently wild conclusions, but they cannot be lightly dismissed,for it is hard to say exactly where they go wrong (if they go wrong at all!).8
8 On this topic see Prior (1967, 149-151); Plantinga (1983); Fine (1985); Linsky and Zalta (1994,1996);Williamson (1998, 2002)."
——Sider, Logic for Philosophers, Oxford, 2010, p307