Dissecting weak discernibility of quanta

• I analyze the weak discernibility program in the foundations of quantum mechanics.
• I identify a shortcoming in all proposed relations that weakly discern quanta.
• I compare my criticism with the circularity objection against weak discernibility.
• I show how to present the question of discernibility in a symmetrized language.
• I show how this maneuver vindicates discernibility of particles by properties.

In this paper I critically examine latest attempts to formalize quantum-mechanical relations that are supposed to weakly discern elementary particles. I argue that all of them make illegitimate and unavoidable reference to numerical identity, and therefore cannot be used as a means to ground (or derive) quantitative facts of identity/distinctness in the qualitative characteristics of quantum systems. I compare my criticism of weak discernibility with the general circularity objection known from the literature, and I show that my argument is more specific, as it is based on a particular criterion which differentiates between legitimate and illegitimate uses of identity. In the end I suggest that we should reevaluate the role of permutation invariance in expressing the facts of qualitative differences between particles. Taking into account the inevitable symmetrization requirement applied to operators in tensor product spaces, it may be claimed that particles of the same type can be absolutely discerned in some accessible states.