Varieties of Rigidity

I am still reading Jason Stanley’s paper. I think that in the end the position he comes to is something close to frigidity which is nice. But first I want to discuss his characterizion of rigidity.

He says,  

Rigidity is a semantic property of an expression. More specifically, it has to do with evaluation of that expression with respect to other possible situations (or ‘worlds’).

I think this is right. Rigidity is not only a semantic property, it is the kind of property wich only shows up in modal contexts. There are many varieties of rigidity out there and he goes on to distinguish them from each other.

1.) Neutral charaterization of rigidity-

a designator d of an object x is rigid, if it designates x with respect to all possible worlds where x exists, and never designates an object other than x with respect to any possible world.

This characterizationis neutral over the issue of what the designator will designate with respect to a possible world where its actual designation does not exist. But it is also neutral between rigidity and frigidity because it is neutral over what counts as a designator. So according to frigidity (1) can be true if the designators are mental names and false if they are linguistic names.  

 2.) Persistent rigid designators- Those

designators d of an object x, which designate x in all worlds in which x exists, and designate nothing in worlds in which x does not exist.

3.) Obstinate rigid designators- Those

designators d of an object x, which designate x in all worlds in which x exists, and designate x in all worlds in which x does not exist; or, more simply, designate x with respect to every possible world.

(2) and (3) differ in the way that they want to treat the designator with respect to a possible world where the designated thng does not exist. The names themselves come from Salmon. Some of the debate that has been going on around here lately can be seen to be over this issue. Kripke’s own view, as Stanley notes, is (3).

 4.) Strongly rigid designators-

those designators d of an object x which exists in all possible worlds, which designate the same thing in all possible worlds (viz. x).

As I have been arguing in the last post, I do not think it is a trivial question whether anything necessarliy exists and so I doubt that there are any strongly rigid designators.

5.) De Jure rigid designators-

An expression is a de jure rigid designator of an object just  in case the semantical rules of the language unmediately link it to that object.

 6.) De Facto rigid designators-

All other rigid designators [i.e. not de jure rigid designators]

Kripke himself casts the distinction in terms of stipulating the reference. A designator is de jure rigid when “the reference is stipulated to be a single object whether we are speaking of the actual world or of a counter-factual situatiuon”. This is the thing that he is actually interested in. A de facto rigid designator is one where a desription ‘happens’ to pick out one unique object in all possible worlds (e.g. ‘the smallest prime number’ picks out The Number Two in all possible worlds.)

Are there such things as de facto rigid designators? I hear ‘the smallest prime number’ used to pick out The Number One back in the Olden Days when people (mistakenly?) thought that The Number One was prime…so maybe what ‘the smallest prime’ designates depends on what we stipulate…I tend to think that all rigid designation (were there any)would be the de jure kind.

At any rate, how doe sthis notion of stipulating the reference connect with (5)’s talk of ‘unmediate links’? Take logic as an example. In logical theory the reference of a given constant C is given by stipulation. We say ‘let C be …’ where ‘…’ is the referent. This stipulative act is licensed by a semantical rule which says that the way the constants reference is determined is via stipulation. We, as it were, just hook the constant onto the thing we want to talk about. In other cases there is a semantical rule which says that the referent is determined by the object(s) that satisfy some description. So, the constants of logic are supposed to be prime examples of de jure rigid designators. And in fact Stanley goes on in thenext section to chronicle how this is in fact historically the way that rigidity first arose, as a theory about the semantics of modal logic.

The real question then is whether or not this story as just told for logic works for English as well. Is ‘Richard’ like C? This brings us to the question of what the job of semantics is and the distinction between P-semantics and L-semantics I introduced earlier but this is already long. Iwill come back to it in another post.


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