The suggestion that particles of the same kind may be indistinguishable in a
fundamental sense, even so that challenges to traditional notions of
individuality and identity may arise, has first come up in the context of
classical statistical mechanics. In particular, the Gibbs paradox has sometimes
been interpreted as a sign of the untenability of the classical concept of a
particle and as a premonition that quantum theory is needed. This idea of a
quantum connection stubbornly persists in the literature, even though it has
also been criticized frequently. Here we shall argue that although this
criticism is justified, the proposed alternative solutions have often been
wrong and have not put the paradox in its right perspective. In fact, the Gibbs
paradox is unrelated to fundamental issues of particle identity; only
distinguishability in a pragmatic sense plays a role (in this we develop ideas
of van Kampen [10]), and in principle the paradox always is there as long as
the concept of a particle applies at all. In line with this we show that the
paradox survives even in quantum mechanics, in spite of the quantum mechanical
(anti-)symmetrization postulates
