Two entities are weakly discernible when an irreflexive and symmetric relation holds between them. That weak discernibility holds in quantum mechanics is fairly uncontroversial nowadays. The ontological consequences of weak discernibility, however, are far from clear. Part of the literature seems to imply that weak discernibility points to a definite metaphysics to quantum mechanics. In this paper we shall discuss the metaphysical contribution of weak discernibility to quantum mechanics and argue that, contrary to part of current literature, it does not (...) provide for a fully naturalistic determination of metaphysics. Underdetermination of the metaphysics still plagues the way of the naturalist. (shrink)