Relativized metaphysical modality

In Karen Bennett & Dean Zimmerman (eds.), Oxford Studies in Metaphysics. Oxford University Press. pp. 189 (2012)
Abstract
It is commonly supposed that metaphysical modal claims are to be evaluated with respect to a single domain of possible worlds: a claim is metaphysically necessary just in case it is true in every possible world, and metaphysically possible just in case it is true in some possible world. We argue that the standard understanding is incorrect; rather, whether a given claim is metaphysically necessary or possible is relative to which world is indicatively actual. We motivate our view by attention to discussions in Salmon 1989 and Fine 2005, in which various data are taken to support rejecting the transitivity of accessibility and modal monism ; we argue that relativized metaphysical modality can accommodate these data compatible with both standard modal logic and modal monism. Noting an analogy with two-dimensional semantics, we argue that metaphysical modality has a complex structure, reflecting what is counterfactually possible, relative to each indicatively actual world. In arguing for the need for relativization, we are broadly on the same side as Crossley and Humberstone and Davies and Humberstone ; our contribution here is, first, to offer distinctively metaphysical reasons for relativization, and second, to show that relativization can be incorporated in ways minimally departing from standard modal logic
Keywords metaphysical necessity  modality
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