 Plantinga defines a possible world to be a state of affairs of a certain sort. A state of affairs for Plantinga is an abstract, fine-grained, proposition-like entity characteristically referred to by sentential gerunds like the earth’s being smaller than the sun.[65]  Some states of affairs obtain and others do not: the earth’s being smaller than the sun obtains; seven’s being the sum of three and five does  not.[66]  Importantly, all states of affairs are necessary beings irrespective of whether or not they obtain. A state of affairs \(s\) is possible if it possibly obtains; \(s\) includes another state of affairs \(s'\) if, necessarily, \(s\) obtains only if \(s'\) does and \(s\) excludes \(s'\) if it is not possible that both \(s\) and \(s'\) obtain; \(s\) is maximal if, for any state of affairs \(s',\) \(s\) either includes or excludes \(s'\). A possible world, then, is a maximal possible state of affairs; and the actual world is the possible world that, in fact, obtains. It is easy to show that, under those definitions, a state of affairs is a possible world just in case it possibly includes all and only the states of affairs that obtain. Since worlds are states of affairs and, for Plantinga, states of affairs are all actually existing abstract entities, their existence is consistent with actualism, as desired.