  We argue that in the case of identical particles the most natural
identification of separability, that is of absence of non-classical
correlations, is via the factorization of mean values of commuting observables.
It thus follows that separability and entanglement depend both on the state and
on the choice of observables and are not absolute notions. We compare this
point of view with a recent novel approach to the entanglement of identical
particles, which allows for the definition of an entanglement entropy from a
suitably defined reduced particle density matrix, without the need of labeling
the system constituents. We contrast this figure of merit with the
aforementioned lack of an absolute notion of entanglement by considering few
paradigmatic examples.
