If possible worlds are conjunctions of states of affairs, as in David Armstrong’s combinatorial theory, then is the empty world to be thought of as the null conjunction of states of affairs? The proposal seems plausible, and has received support from David Efird, Tom Stoneham, and Armstrong himself. However, in this paper, it is argued that the proposal faces a trilemma: either it leads to the absurd conclusion that the actual world is empty; or it reduces to a familiar representation of the empty world in which the concept of a null conjunction plays no role; or it needs to make room for the null individual of certain non-classical mereologies.
Bibliographical noteThis paper was read by four anonymous referees for this journal, three of whom provided comments that were helpful in revising earlier drafts. At an earlier stage, I also received helpful comments from Ethan Brauer, Leon Horsten, and Dan Marshall.
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