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Barcan formula

Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


L ogic A principle in quantified modal logic, introduced by the American logician Ruth Barcan Marcus . It states that if possibly there exists something that is A, then there is something that is possibly A. That is, ◊(∃x)A strictly implies (∃x)◊A. This is also true for its converse: (∃x)◊A strictly implies ◊(∃x)A. The Barcan formula also includes the following thesis: If everything is necessarily A, necessarily everything is A. That is, (∀x) □ A ⊃ □ (∀x)A. The formula is rejected by Kripke and Rescher by appeal to the theory of possible worlds , for in this formula the antecedent might be true of the actual world, but its consequent might be false in certain possible worlds. “… The Barcan Formula stipulating the implication from ◊(∃x)φx to (∃x)◊φx.” Rescher, A Theory of Possibility ... log in or subscribe to read full text

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