Why Contingentist Actualists Should Endorse the Barcan Formula

Acta Analytica 38 (1):133-159 (2023)
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Abstract

On its usual interpretation, the Barcan Formula—◊∃xBx → ∃x◊Bx—says that, if there could have been something that is such and such a way, then there is something that could have been that way. It is traditionally held that contingentist actualists should—indeed, must—reject the Barcan Formula. I argue that contingentist actualists should—indeed, must—endorse the Barcan Formula, at least assuming a standard, Tarskian conception of truth and truth preservation. I end by proposing a logic for contingentist actualists that validates the Barcan Formula. This logic has the surprising feature of also validating the Converse Barcan Formula, □∀xBx → ∀x□Bx, while still invalidating related formulas—such as □∀x□∃y x=y (NNE)—that contingentist actualists should reject. It does this by employing models with fixed domains but assignments to the identity predicate that vary across worlds.

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Nicholas Rimell
Chinese University of Hong Kong

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A World of States of Affairs.D. M. Armstrong - 1996 - New York: Cambridge University Press.
Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
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On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.

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