“The designatum must first be picked out in Î± by whether it meets the descriptive requirements (with or without the indexing) there in Î±: but the purpose of the indexing is to keep the term referring, with respect to other worlds, to that same item picked out originally in Î± by virtue of meeting the right requirements there.”
“Here are some considerations in favor of saying that an expression could be rigid de jure without directly referring to its designatum.”
“Here you use the description to fix the reference, not as a synonym: whatever individual is most filled with joy is the designatum, even when we are discussing worlds in which that same individual is glum.”
“In other places, Kripke seems to have in mind another account of rigidity: one according to which a rigid designator designates its object in every possible world, whether or not the designatum exists in that world.”
“On one such account, a rigid designator designates its designatum in every possible world containing the designatum and in other possible worlds the designator fails to designate.”
“That is because some expressions designate rigidly by means of describing the designatum: e.g.,”
“When we evaluate these sentences with respect to other worlds, we do not seem to admit that the designatum changes, as it would if names were non-rigid descriptions taking the proper scope in modal contexts.”
“Nam profecto aut metus aut injuria te subegit,  Silane, consulem designatum, genus poenae novum decernere.”
“Nobilissimum designatum, participem quoque regni ani, successoremque creavit. ”
“According to some philosophers (Salmon 1981, p. 33 note 35), it would be metaphysically possible to coin non-rigid directly referential expressions, by devising some means of assuring that they change their designatum from world to world; even this claim may be controversial (cf. Soames 2002, pp. 264 “ 5; King”
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