This is a systematic review of the concept of indistinguishability, in both classical and quantum mechanics, with particular attention to Gibbs paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of classical indistinguishability, notwithstanding the widely-held view, that classical particles can always be distinguished by their trajectories. The last section is about the notion of object more generally, and on whether indistinguishables should be thought of as objects at all.

The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs’paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguishability, in quantum mechanics but not in classical mechanics, forces a change in statistics. The answer, illustrated with simple examples, is that the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. The (...) relevance of names, or equivalently, properties stable in time that can be used as names, is also discussed. (shrink)