Argumenta – Journal of Analytic Philosophy


S4 to 5D [Special Issue]

Issue: Issue 4 • Author/s: Takayashi Yagisawa
Topics: Philosophical logic

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…