For entropy of mixing to exist, the putatively mixing molecular species must be chemically or physically detectably distinct. Thus arises the so-called "Gibbs paradox", as follows. If molecular species are identical, there is no entropy change on mixing them, because, defined in thermodynamic terms, there is no mass transfer, and thus no thermodynamically recognized process of mixing. Yet the slightest detectable difference in constitutive properties between the two species yields a thermodynamically recognized process of transfer with mixing, and a possibly considerable entropy change, namely the entropy of mixing.