Argumenta – Journal of Analytic Philosophy

The modal logical axiom 4 is widely accepted. It is the characteristic axiom of the modal logical system S4, which is subsumed under the most popular modal logical system S5. Axiom 4 is equivalent to ◇◇P → P (“If possibly possibly P, then possibly P”), which requires that the accessibility relation between worlds be transitive. There is a powerful argument (Hugh Chandler 1976, Nathan Salmon 1981, 1989) against axiom 4. It rests on the thought that an ordinary object could have had a slightly different origin from its actual origin but could not have had an origin very different from its actual origin. By constructing a sorites-like sequence of possible worlds at which the origin of a given object shifts incrementally along the sequence, the argument concludes that accessibility is not transitive, i.e. that what is possibly possible may not be possible. A recent attempt to defend S4 from this argument (Murray and Wilson 2012) proposes that we abandon the absolute notion of possibility and instead accept a world-indexed notion of possibility; each world comes with its own version of possibility. I offer a different defense of S4, which preserves both axiom 4 and the absoluteness of possibility. Its key move is to postulate objects as extended not only in physical space-time but in logical space as well, that is, as “five-dimensional” worms. Since S4 and the absolute notion of possibility are very intuitive, quite useful, and widely well regarded, and since my proposal saves both of them, I take the proposal to constitute an argument in favor of “five-dimensionalism.”


S5 is the most popular modal logical system among modal metaphysicians. S4 is weaker than S5. So, anyone who accepts S5 should also accept S4. But there is trouble with S4. Or so argue Hugh S. Chandler and Nathan Salmon. Chandler’s argument is directed against Alvin Plantinga’s claim that nothing is possible at some possible worlds and not possible at others. Chandler aims to establish “that what is possible varies from world to world.”


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