Another Look at Armstrong's Combinatorialism
Sider (Ted)
Source: Noûs 39 (2005): 680–696
Paper - Abstract

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Author’s Introduction

  1. The core idea of David Armstrong’s combinatorial theory of possibility is attractive. Rearrangement is the key to modality1; possible worlds result from scrambling bits and pieces of other possible worlds. Yet I encounter great difficulty when trying to formulate the theory rigorously, and my best attempts are vulnerable to counterexamples.
  2. 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 figures prominently in what follows.
  3. Section 1 of this paper reconstructs Armstrong’s theory, section 2 defends it from criticisms due to Fraser MacBride and Holly Gail Thomas, and section 3 gives a number of objections to that theory. Section 4 develops yet another objection, building on work by David Lewis.


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