Modal status of propositions depends on the logical framework adopted, and S5 modal logic—which licenses the move from possibility to necessity for necessary beings—is not the uniquely correct system.

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Logical framework(logic): A complete system of rules and symbols that logicians use to check whether arguments are valid, like a standardized language for thinking.
Modal logic(logic): A system of logic that deals with concepts like possibility, necessity, and what could or must be true.
Modal status(as used in metaphysics and logic): Whether something is necessary (must be true), possible (could be true), or contingent (just happens to be true). 'Modal' refers to these kinds of distinctions about how things *could be* versus how they actually are.
S5 modal logic(The system under which Adams's modal argument reaches its absurd conclusion; the weaker system B also suffices): A modal logic system in which the axiom 'possibly necessarily P entails necessarily P' holds, making the accessibility relation for possible worlds an equivalence relation

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