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The following quote from the article is inaccurate:

The "could" here is important to note: rigid designation is a property of the way terms are used, not a property of the terms themselves, and a phrase such as "the first Chancellor of the German Empire" could be used rigidly (if one were to say, "The first Chancellor of the German Empire was a free agent like everyone else: he could have decided never to go into politics"

A description never rigidly designates, and in the quoted example, what is rigidly designating is the personal pronoun 'he', which is referring specifically to the person that happened to be the first Chancellor of the German Empire. What is not rigidly designating is the desciption, and this is quite easily seen.

In Kripke's theory, identities between rigid designators are necessary. If water=h20, then necessarily water=h20. But an identity involving a description is never necessary. It is not the case that if the first Chancellor of the German Empire was Otto von Bismarck, then necessarily the first Chancellor of the German Empire was Otto von Bismarck. It is possible that Bismarck may have died early and so never became Chancellor. Hence, the statement is not necessary because one of the terms, the description actually, does not rigidly designate.

Perhaps what is being confused is rigid designation and reference-fixing. I have remedially edited the body of the article accordingly. Nortexoid 04:36, 19 Oct 2004 (UTC)

This is not an accurate criticism. Looking back at the relevant passages in Naming and Necessity, I see that there is an accurate criticism to be made of the passage as I wrote it: the claim is more controversial than I remembered, and Kripke in particular isn't convinced. But there certainly are philosophers who take definite descriptions to sometimes be used rigidly. Here's Kripke:
I assume Russell is right in that definite descriptions can at least sometimes be interpreted nonrigidly. As I mention on page 59 footnote 22, some philosophers think that, in addition, there is a rigid sense of definite descriptions. As I say in the latter footnote, I am not convinced of this, but if these philosophers are right, my principal thesis is not affected. It contrasts names with nonrigid descriptions, as advocated by Russell. See Section 2, pp. 258-61 of my paper, "Speaker's Reference and Semantic Reference" ... for a brief discussion of the relation of the idea of rigid definite descriptions to Donnellan's "referential" descriptions. I also discuss the relation of both of these to the notion of scope. (Naming and Necessity, pp 6-7n8)
Some philosophers have thought that descriptions, in English, are ambiguous, that sometimes they non-rigidly designate, in each world, the object (if any) satisfying the description, while sometimes they rigidly designate the object actually satisfying the description. (Others, inspired by Donnellan, say the description sometimes rigidly designates the object thought or presupposed to satisfy the description.) I find any such allegedly ambiguities dubious. I know of no clear evidence for them which cannot be handled either by Russell's notion of scope or by the considerations alluded to in footnote 3, p. 25. (pp. 59-60n22)
Since Kripke isn't himself convinced, and Kripke has as good a right as anyone to figure out how the term "rigid designator" is used, the passage needs to be qualified. But it is no less correct to claim straight up that definite descriptions can't rigidly designate, since it has been argued that they can.
What cannot be argued? Does it really matter that Joe Shmoe in some journal article argued that descriptions can sometimes rigidly designate? I think it is mostly important to stick with Kripke's view of rigid designation since it is in fact his view. It might be more fitting to simply state briefly that some have argued that descriptions may rigidly designate (and cite sources), but there should not be a cumbersome explanation of it in the article itself.
As for the specific objection to the example used to exposit: you can avoid the conclusion that "the first Chancellor &c." is rigidly designating in that specific sentence by putting the rigid designation on the shoulders of "he" instead, but there is no reason to think that such a solution can be applied to all relevant example sentences. Here's a trivial rewrite of the sentence that I used as an example before: "The first Chancellor of Germany could have decided never to go into politics." (Similarly, "our first President could have died in smallpox in his youth, and what would have happened to us then?", "the painting you see on the wall might have been lost forever, if the bombing had been only a little to the east," etc.)
I do not see how those examples show that descriptions can be used rigidly. What it shows is that we understand who the speaker is referring to when he gives the description since, in the actual world, there is only one person satisfying that description. But in some other world, that sentence may or may not be true if the description is not satisfied or satisfied by a different person.
Your example of the painting is entirely different. It looks prima facie to be a description but it is actually one of ostension; "The painting you see on the wall (pointing), might have been lost forever". Identifying objects by ostension is always rigid, and this is in fact how baptizing is done.
"But an identity involving a description is never necessary." Is "The man with the glass of champagne in his hand is Jones" a contingent statement or a necessary statement? Well, it depends on whether you are talking about the man himself or about whoever it is who happens to have the glass of champagne in his hand.
It shouldn't depend on who the speaker is intending to refer to, which is actually the point. If it is ambiguous as to who the speaker is referring to when he uses a description it is because it could possibly be someone else; in other words, the description does not rigidly designate. The man may not have champangne in his hand even though the speaker thinks he does and he is attempting to refer to him. If he does not have champagne in his hand, then it is false that 'the man with champagne in his hand is Jones -- i.e., it is not necessarily true.
If definite descriptions never designate rigidly, then the only way get to talking about the man himself is to invoke something like Russell's notion of scope. But I think you'd need to give some independent reason for thinking that you can't use "the man with the glass of champaign in his hand" rigidly. (Of course, in other possible worlds where Jones is not the man with the glass of champagne in his hand, someone who said "The man with the glass of champagne in his hand is Jones" would be speaking falsely, but so what? That's no more convincing in either direction than the fact that Hesperus might not be called "Hesperus" in some possible worlds.)
There are several ways of picking out the man. One, call him by his name. Two, by ostension - point him out ("that man..."). Three, use a description such that him and only him satisfies it, but that does not imply the rigidity of that description simply because it actually denotes someone in the actual world. Why? Because it does not denote the same person in every world. In some possible world he does not have champagne in his hand, someone else or nobody does.
In light of all this (not to mention the non-commital nature of Kripke's own doubts), I am reinstating the passage that was excised, with edits to qualify it as disputed. Thanks for raising the point. Radgeek 07:48, 11 Dec 2004 (UTC)
I cannot agree with keeping that passage in the article. It isn't accurate or it is at least confusing. I suggest removing it and putting something along the lines of "It has been argued that definite descriptions may rigidly designate. Kripke is not convinced. See so-and-so. Nortexoid 03:31, 13 Dec 2004 (UTC)

Regardless of the conclusion to the discussion above, some definite descriptions are quite trivially rigid. Like "The smallest prime number". (This is why the distinction between de jure and de facto rigidity makes sense.) I am sure that Kripke would also accept that a description like "The person who is actually the current president of the USA" is rigid. So the subject of the discussion in the article should not be whether definite descriptions can be rigid, but whether descriptions that normally are nonrigid may have a rigid interpretation. —Preceding unsigned comment added by Kjema (talkcontribs) 21:27, 30 April 2008 (UTC)[reply]

Another interpretation

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Perhaps what he meant was that terms like "the holy roman empire" (with "the" at the beginning) could count as proper names, and not as descriptions (see the 1st lecture of naming and necessity)

that works for your example because 'the holy roman empire' is a name, but not for 'the 1st Chancellor of the German Empire', which is clearly a description. Nortexoid 23:02, 23 Nov 2004 (UTC)

Descriptions

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They're useful for reference fixing and initial baptisms -- e.g. "This baby boy who I am pointing at who is the son of so and so is named John". Nortexoid 02:47, 12 Dec 2004 (UTC)

Present criticisms

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The article seems to do a good job at presenting Kripke's positive views. However, like anything else, his views have been criticized. Philopshers of science have argued for example the Water is NOT necessarily H20 is all possible worlds. Followers of Wittgenstein, I get the impression, do not accept Kripke's views. I think both Ayer and Quine are anti-essentialists too. Perhaps the article can provide criticism of Kripk'e views.

Some of the classical criticism should also be mentioned. Like Quine's accusation that the notion of rigidity is circular, the suggestion that our intuitions about the way names affect truth value can be accounted for as a scope phenomenon, and Gareth Evans' refusal to distinguish between rigid designation and reference.

David Miller also criticised Kripke's distinction between rigid and non-rigid designators in "What's in a Numeral", he claimed that the distinction between rigid and non-rigid designators is either circular or question begging. 155.192.180.10 (talk) 14:23, 29 October 2017 (UTC)[reply]

Obstinate vs persistent rigidity

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I think it might be a good idea to remove the distinction between persistently and obstinately rigid designators from the introduction, and present i later instead. It looks like it is uncontroversial that there are any obstinately rigid designators, which it isn't.

Vivid designator

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Mostly because I wanted to know more about it, I created a page of the term vivid designator. I am hoping for some help with it, or some additional information on it. Since the terms are so closely related, I thought I'd mention it here. — Preceding unsigned comment added by Fan Singh Long (talkcontribs) 09:09, 5 February 2012 (UTC)[reply]