  As another example of possibilist/actualist difference, consider \(\exists x\Box P(x) \supset \Box \exists xP(x)\). With possibilist quantifiers, this is valid and reasonable. It asserts that if some possibilia has the \(P\) property in all alternative states, then in every alternative state some possibilia has the \(P\) property. But when possibilist quantification is replaced with actualist, \(\exists^{E}x\Box P(x) \supset \Box \exists^{E}xP(x)\), the result is no longer valid. As a blatant (but somewhat informal) example, say the actual state is \(\Gamma\) and \(P\) is the property of existing in state \(\Gamma\). Then, at \(\Gamma , \exists^{E}x\Box P(x)\) says something that actually exists has, in all alternative states, the property of existing in the state \(\Gamma\). This is true; in fact it is true of everything that exists in the state \(\Gamma\). But \(\Box \exists^{E}xP(x)\) says that in every alternative state there will be an actually existent object that also exists in the state \(\Gamma\), which need not be the case.