Another Look at Armstrong's Combinatorialism

Abstract

The core idea of David Armstrong’s combinatorial theory of possibility is attractive. Rearrangement is the key to modality; possible worlds result from scrambling bits and pieces of other possible worlds. Yet I encounter great dif culty when trying to formulate the theory rigorously, and my best attempts are vulnerable to counterexamples. The Leibnizian biconditionals relate possibility and necessity to possible world and true in: p is possible iff p is true in some possible world p is necessary iff p is true in all possible worlds Given an account of the latter notions, one can reduce the former via the biconditionals. In A Combinatorial Theory of Possibility, and then again in A World of States of Affairs, Armstrong characterizes possible worlds as rearrangements of elements of the actual world. But he says comparatively little about true in. This omission gures prominently in what follows.

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