High Quality Content by WIKIPEDIA articles! In quantified modal logic, the Barcan formula and the converse Barcan formula state possible relationships between quantifiers and modalities. The Barcan formula is a natural axiom to consider in quantified forms of Clarence Irving Lewis's systems of modal propositional logic. It was introduced as an axiom by Ruth Barcan Marcus, in the first extensions of modal propositional logic to include quantification.Related formulas include the Buridan formula, and the converse Buridan formula.In n English, the statement reads: If everything is necessarily F, then it is necessary that everything is F. The Barcan formula has generated some controversy because it implies that all objects which exist in every possible world (accessible to the actual world) exist in the actual world. In other words, the domain of any accessible possible world is a subset of the domain of the actual world.

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