Infinitely Iterated Possibility: Worlds Reachable Only With Infinitely Many Transfers

Abstract

Nathan Salmon (1989) famously argues that there are impossible worlds that are nevertheless possibly ... possibly possible. Modifying his argument and utilizing a fractal structure called the Koch snowflake, I argue that there are impossible worlds that are possibly ... possibly possible not for any finite degree of nesting but only for an infinite degree of nesting. To accommodate this result, I suggest that the syntax and semantics of modal logic be augmented so that it allows infinite iterations of modal operators.