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Exactly what it says on the tin: Do abstract objects, like universals for instance, necessarily exist in all possible worlds? To my knowledge, David Lewis held to the opinion that they did (And that as such they existed "at" all possible worlds, rather than "in" all possible worlds as proper parts of those worlds, to conform to his modal realism). But can there be a sense in which universals themselves are contingent and as such vary between possible worlds? If one conceives of a "World" as simply being a maximal consistent set of propositions, then that seems perfectly feasible to me, but I haven't seen any literature expounding on the possibility.

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  • See SEP, Combinatorialism:"Wittgenstein famously asserted that the world is the totality of facts, not of things. The combinatorialist spells out Wittgenstein's aphorism explicitly in terms of an ontology of objects (a.k.a., particulars), universals (a.k.a., properties and relations), and facts... the existence of both particulars and universals depends on their “occurring” in some fact or other... the worlds of combinatorialism are simply rearrangements of the universals and particulars of the actual world."
    – Conifold
    Commented Apr 22 at 0:47

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