 Furthermore, a term might rigidly designate under one interpretation of rigidity but non-rigidly designate under a different interpretation of rigidity: thus, ‘Hesperus = Phosphorus’ is apparently not epistemically necessary, even though it seems alethically and temporally necessary.  Accordingly, ‘Hesperus’ and ‘Phosphorus’ are plausibly thought not to be epistemically rigid, in which case, as Fitting and Mendelsohn (1998, p. 219) observe, “it is hard to see whether there are any rigid designators under the epistemic reading.”  A counterpart construal (see below) might be offered more plausibly for epistemic possibility than for temporal or alethic possibility, as Kripke himself sometimes suggests (Rabern 2018, pp. 12–13): when we say that Hesperus might for all we know have turned out not to be Phosphorus, we seem to have in mind a possible world in which something else—a counterpart—is present in the morning or evening, not Hesperus (Phosphorus).  This entry will address an alethic interpretation of rigidity for the most part.