  It is important to note that the possible worlds of abstractionism do not yield a reductive analysis of modality. The reason for this is clear: abstract possible worlds are defined in irreducibly modal terms — a possible world is an SOA that (among other things) possibly obtains; or a set of propositions such that it is possible that all of its members are true; or a property that is possibly exemplified; and so on. Hence, unpacked in terms of the abstractionist's definitions, the possible world truth conditions for modal propositions are themselves irreducibly modal. For example, when we unpack Plantinga's definition of a possible world in the semantic clause for sentences of the form ⌈◻ψ⌉ in order to derive the truth condition for (17), ‘□∀x(Gx → Mx)’, we end up with this: 