Does everything have at least one rigid designator?

Question

Put antother way

Proposition 1: for anything that exists in this world I can find/construct, even if just by assertion, a rigid designator that applies to it.

Proposition 2: like proposition 1 but over all possible worlds.

What are the status of these propositions?

I think that in the context of reading Kripke, a definition of "anything" in this would be "any object/entity that we can discriminate/delineate via natural language". This is based on the position that if we can talk about it in a sensible way, then we could apply a proper name to it, and thus it would have a rigid designator.

Answer 1

I took Kripke to be saying that we can rigidly designate something, and we can rigidly designate anything precisely when we pick that thing out across all possible worlds.

See http://plato.stanford.edu/entries/rigid-designators/

A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else.

Though an important qualification is that a name that rigidly designates from the standpoint of our world may not be a name that would rigidly designate from a different world, but it does for us.

Proposition 1 seems to follow tautologically from the definition. Proposition 2 seems to suffer from two important ambiguities:

1. It is not clear that an event of rigid designation has occurred.
2. The meaning of the phrase "over all possible worlds" is unclear vis-a-vis the act of rigid designation.

I could probably write more ... but it's been 8 years since I've read Kripke, and I'm not quite sure where you're going with this.

Or to word it another way in answer to your title question, everything could have a rigid designator if anyone bothered to assign one to it, which often happens in the form of a name that is given to pick it out in all possible worlds from the privileged location of this world.