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.”