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Axiom S5 is the distinctive axiom of the S5 system of modal logic and says that if possibly necessarily p, then necessarily p. If the modality here is what Alvin Plantinga calls "broadly logical" necessity and possibility, then an argument for the axiom can be given as follows. If possibly necessarily p, then there is a possible world w at which p necessarily holds. Then, it is true at w that p is a broadly logically necessary truth, something whose negation would in a broadly logical sense be self-contradictory. But if something is self-contradictory at some possible world, then it is self-contradictory at all worlds, and Plantinga holds that this is true even in the case of broadly logical self-contradictions as well.
Axiom S5 is also at the heart of Plantinga's ontological argument.
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