The reversibility objection against the Second Law of thermodynamics viewed,and avoided,from a logical point of view

In this paper we offer a formal-logical analysis of the famous reversibility objection against the Second Law of thermodynamics. We reconstruct the objection as a deductive argument leading to a contradiction, employing resources of standard quantified modal logic and thereby highlighting explicit and implicit assumptions with respect to possibility, identity, and their interaction. We then describe an alternative framework, case-intensional first order logic, that has greater expressive resources than standard quantified modal logic. We show that in that framework we can account for the role of sortals in possibility judgments. This allows us to formalize the relevant truths involved in the reversibility objection in such a way that no contradiction ensues. We claim that this analysis helps to understand in which way the Second Law is, specifically, a law of thermodynamics, but not of systems of particles in general.