 Several remarks on this argument are in order. First, its conclusion is very strong: it says that any entity that in fact exists or that could have existed exists necessarily. There is no contingent existence. This goes far beyond the claim that there are genuine identities across worlds. (Williamson (2002) defends this conclusion on independent grounds.) Second, the argument does not offer an explanation of how transworld identities are possible; it insists only that there are genuine transworld identities. (Nevertheless, the metaphysical picture that can most naturally be ‘read off’ the constant-domain semantics treats properties-at-a-world as relations between particulars and worlds, as on McDaniel’s modal realism with overlap (McDaniel 2004), discussed in Section 1.2 above.)