  The Gibbs paradox has frequently been interpreted as a sign that particles of
the same kind are fundamentally indistinguishable; and that quantum mechanics,
with its identical fermions and bosons, is indispensable for making sense of
this. In this article we shall argue, on the contrary, that analysis of the
paradox supports the idea that classical particles are always distinguishable.
Perhaps surprisingly, this analysis extends to quantum mechanics: even
according to quantum mechanics there can be distinguishable particles of the
same kind. Our most important general conclusion will accordingly be that the
universally accepted notion that quantum particles of the same kind are
necessarily indistinguishable rests on a confusion about how particles are
represented in quantum theory.
