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However, if one designator in a true identity statement but not the other rigidly designates an entity like H2O diagonally, then the statement is a posteriori, as 'Water = H2O' is.
This would obviously result in taking each rigid designator (in today's terminology) to express an intuition.
It follows that no name of the piece of clay c can be a rigid designator in the standard sense.
Assuming that Kripke's arguments against widescopism are successful, it might appear that any statement S containing a proper name cannot have the same content as a statement S′ that differs from S just in the respect that a proper name in S is replaced by a non-rigid designator in S′.
In order to fly to the VOR station, you would first twist the OBS knob until the needle is centered and the white triangle registers, pointing next to the "TO" designator (in the opposite direction, or up, from the "FR" designator).
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Kripke would say that if both designators in an identity statement rigidly designate the same entity, then the statement is necessarily true, as 'Water = H2O' is.
A two-dimensionalist naturally understands this claim as one that concerns horizontal rigidity: for her, if both designators in an identity statement rigidly designate the same entity horizontally, then the statement is necessarily true, as 'Water = H2O' is.
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.
Intuitively, rigid designation is needed on the part of both designators if there are to be true "theoretical identity statements": statements in which a designator designates by way of expressing explicitly in some manner one of the designatum's theoretically interesting essences.
They need not be rigid designators in models where the possible worlds represent epistemically alternative states.
And again, the rigidity of designators in a true theoretical identity statement is sufficient for the statement's necessity.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com