We introduce into classical mechanics the concept of non-discerned particles
for particles that are identical, non-interacting and prepared in the same way.
The non-discerned particles correspond to an action and a density which satisfy
the statistical Hamilton-Jacobi equations and allow to explain the Gibbs
paradox in a simple manner. On the other hand, a discerned particle corresponds
to a particular action that satisfies the local Hamilton-Jacobi equations. We
then study the convergence of quantum mechanics to classical mechanics when
hbar -> 0 by considering the convergence for the two cases. These results
provide an argument for a renewed interpretation of quantum mechanics
