Rigid designation is for proper names. We can use "water" as a proper name like this:

The water in the pool could have been more alkaline.

that bolded section can serve as a rigid designator because we know which water is being discussed. And here:

Water is H20. — frank

My objections have been more around natural kinds as rigid designators, not proper names. Kripke's example "water is H2O" is about a natural kind.

My objections have been more around natural kinds as rigid designators, not proper names. Kripke's example "water is H2O" is about a natural kind. — Richard B

Gotcha. Do you think it's true that water is H20?

If you want a reply on this, you are going to have to explain what you are claiming. Are you trying to say something like: "If 'The cat is on the mat' is false (a proposition with sense), how does this imply anything about 'The cat is on the mat or the cat is not on the mat' (a tautology without sense)?" If so, the answer is straightforward: it doesn't imply it in the usual sense. Rather, the tautology is true independently of whether the contingent proposition is true or false. The relationship isn't one of implication but of logical independence—which is precisely the point about necessary truths being "empty" of empirical content. — Banno

OK, to understand what you are saying here, when Kripke says, "Well, if something is false, it's obviously not necessarily true." he is not saying that when something is contingently false, you can infer that it is not necessary true. But that the relationship has something to do with logical independence. Or is that what the Tractatus says, and Kripke would disagree with? I would think the later, and hence my discomfort.

"Water is H2O" is statement without context my friend. If the term "water" is being used like "Dihydrogen monoxide" then it is a stipulation and thus analytically true. There is no difference between "water is H20" and "Dihydrogen Monoxide is H2O". If you are using it as a chemist may use it, then it is about composition, not identity. You can call any liquid you like by the name of"water", but an scientific analysis will tell you the composition. And even if you discover that it is mainly composed on H2O molecule, you can still call that liquid by another name depending on the context of the scientific activity.

Kripke specifically says the statement he's analyzing, ("H20 is water") is an expression of a scientific discovery (N&N pg. 128). Still, this is too foggy for you. I guess when he earlier talks about Kant saying that gold is a yellow metal, you'd object that Kant isn't asserting something meaningful because we don't know for sure what gold is.

I can't follow that. Is there a typo?

Something is necessarily true iff it is tru in every case. Hence, if it is false in a given case, it cannot be necessarily true. I can't see you disagreeing with that.

And if something is contingent, then it is not necessary. I can't see you disagreeing with that.

Both Kripke and the Tractatus would agree here.

. , what if we revers the wording - is a glass of pure H₂O a glass of water?

I say yes. What say you?

I'd say so.

Another thing to bear in mind, is the relationship between Kripke's axiom x=y → □x=y in relation to his "Naming and Necessity" lectures that he gave in 1970 on the one hand, versus Kripke's resolution of his sceptical paradox on the other, that he discussed in lectures in the late seventies that led to the 1982 publication "Wittgenstein on Rules and Private Language".

Notably, Kripke's positions on both positions seem on the surface to come into collision, that might suggest an "early Kripke" with potentially radically different views from an emerging "later Kripke", that parallels the distinction between the early/late Wittgenstein.

Recall that it only hit Kripke later on in his career, that the truth of a mathematical formula might refer to intersubjective social and environmental assertibility conditions that exist independently of the speaker's subjective mental states and personal use of the formula. So the problem for the later Kripke is how to still make sense of x=y → □x=y in light of the skeptical rule following paradox that he later readily acknowledges, and whether it forces him to abandon this axiom.

Actually, in this regard the equivalent contrapositive form ¬□(x = y) → x ≠ y shines brighter in the face of semantic skepticism, in saying something like "If x isn't necessarily asserted to be equal to y in the future, then I cannot in good conscience declare x to be definitionally equal to y today". And since it is impossible to know in advance what terms will necessarily be intersubstitutable after the next theory change, then one can deduce from the contrapositive of Kripke's axiom that equality 'in good conscience' is purely reflexive: x=y → x=x. In which case, Kripke's axiom has an anti-metaphysical reading on the understanding that no object is necessarily identical to any other object, in which case Kripke's axiom becomes structurally synonymous with propositional equality in intensional type theories,which is precisely of the form x=y → x=x, indicating that terms x and y are only equal if they reduce to the same term after term rewriting.

Also recall that the early Kripke proposed the category of a priori contigent propositions. This category is much more resilient to theory change and skeptical paradoxes than the necessary a posteriori category, since they represent the fact that our axioms are perpetually subject to reinterpretation and even revision in light of new information. In light of semantic skepticism, the expression ¬□(x = y) → x ≠ y very much looks like a metalogical theorem stating that equality is a priori contigent - an interpretation that flips Kripke's rigid desgination on its head by interpreting it as implying that identity is non-rigid via a denial of the consequent.

"Let's call something a rigid designator if in every possible world it designates the same object, a nonrigid or accidental designator if that is not the case. Of course we don't require that the objects exist in all possible worlds" — Richard B

Notice this condition, it's a rigid designator "if" it designates the same object in every possible worlds. The issue is that possible worlds are abstractions, so there are no objects in any possible worlds. This makes "rigid designator" useless right from the start, unless we go to some form of concretism. But concretism disallows such transworld identity anyway, for other very clear reasons. So "rigid designator" is completely useless.

Here is the way that Wittgenstein elucidated this issue of identity in "Philosophical Investigations", starting from 253.

253. When I say "another person can't have my pains", what is the criteria of identity? Consider: "This chair is not the one you saw here yesterday, but is exactly the same as it". But if it makes sense to say "my pain is the same as his", then it makes sense to say that we both have the same pain.

254 The substitution of "identical" for "the same" is an "expedient in philosophy". The question for the .philosopher is to give an account of the temptation to use a particular phrase. What, for example mathematicians are inclined to say about "mathematical facts", is not philosophy, but "something for philosophical treatment".

255. "The philosopher's treatment of a question is like the treatment of an illness."

256. Now, how can I give an account of my inner experiences? How can I use words to refer to my inner sensations? I could use natural expressions, but suppose there were none, and I had to "simply associate names with sensations".

Richard B, please reflect on what has been exposed here. There is a problem of "identity" when referring to inner things such as sensations. We cannot employ the same criteria of "identity" which we use when referring to physical objects like the chair. This is because in the case of physical objects we distinguish between "identical" and "the same", but we cannot make that distinction in reference to inner things like sensations. So, with the physical object, there is a chair here today, which is "identical" to the chair which was here yesterday, but it is not "the same" chair, if someone switched two identical chairs. In the case of inner things, if I feel a pain today which is "identical" to the one yesterday, I call it "the same" pain, and the two terms "identical" and "the same" are used interchangeably.

In this way, as described by 253, it makes sense to say "pain" may refer to the same thing for me, as it does for you, therefore you and I feel the same pain, and refer to the same thing when we say "pain". However, this only works if we have the criteria required for justification.

So this matter of criteria is the key point for transworld identity, and specifically the notion of "rigid designator". To signify the object which the rigid designator refers to requires some criteria. This would produce the need for necessary (essential) properties, thereby compromising the usefulness of the possible worlds semantics. We need to allow that the designated object has nothing essential, to cover all the possible worlds. But this denies the possibility of criteria. Then, whatever it is, the supposed object, which is designated by the rigid designator, is completely unintelligible in the way described by Wittgenstein's "private language". It is a private, inner thing, with no criteria for identification, hence no way of knowing the thing being referred to.

So, after laying out this platform, Wittgenstein proceed to talk about the problem of producing such criteria of identification, which I call justification of the use of the name.

Kripke's example, I like it because it seems rather apropos for everyday conversations we have about everyday objects. — Richard B

Kripke's example is naive, and not at all a fair, or an accurate representation. He says:

"I have the table in my hands, I can point to it, and when I ask whether it might have been in another room, I am talking, by definition, about it. I don't have to identify it after seeing it through a telescope."

What he says here is demonstrably wrong and deceptive. The spoken about object is actually defined as "the table in my hands". Therefore the question about "whether it might have been in another room" must be answered with "No". It is impossible that "the table in my hands" could be in another room because then it would not be ""the table in my hands". The point is that if we adhere to what he says "I am talking by definition, about it", where "it" clearly refers to the table in his hands, then it is impossible that this object is in another room. If it was in another room, it would not be the designated object "the table in my hands".

So Kripke just makes a deceptive use of language, to produce the appearance that the table in his hands could also be in another room. Clearly though, if we adhere strictly to the example, this claim is false. The object defined as ""the table in my hands" could not possibly be in another room, because that would not be consistent with the definition.

And "rigid designator" turns out to be a nonsensical, unintelligible proposal, for the reasons demonstrated by the private language argument. If the designated object is identified by physical existence "the table in my hands", then it cannot be in other possible worlds. And if we remove the physical existence, then it's a private object with no criteria for identification. Any criteria for identity (essential properties) denies certain possible worlds as not possible, arbitrarily compromising the use of "possible worlds".

I can conceive going to a community and asking for a glass of pure H2O and the waiter looking at me with puzzlement. I was thirsty so quickly change my strategy and I ask for a glass of water.

I can also conceive going to a community, maybe too scientifically literate, and asking for a glass of pure H2O, but this time the waiter gives me an incredulous look. The waiter explains that they only have 99.8% H2O, 10ppm Na, 30 ppm Ca, 2 ppm Mg, 5 ppm SO4, 25 ppm Cl, 30 ppm HCO3, 0.1 ppm Fe, 300 ppm HDO, and 20 ppm D2O. He also explains to me that there is some uncertainty in these numbers but can provide those values if requested. I was thirsty so I drank this cornucopia of chemicals, even with this analytical uncertainty.

Back at you

I can conceive some gold is Au if fool’s gold gets $4500 oz. Do I need guidance from possible world semantics to clarify that my use of “some” needs correction?

What say you?

Back at you — Richard B

Ok. That's fine. Is a glass of 99.8% H2O, 10ppm Na, 30 ppm Ca, 2 ppm Mg, 5 ppm SO4, 25 ppm Cl, 30 ppm HCO3, 0.1 ppm Fe, 300 ppm HDO, and 20 ppm D2O, a glass of 99.8% water, 10ppm Na, 30 ppm Ca, 2 ppm Mg, 5 ppm SO4, 25 ppm Cl, 30 ppm HCO3, 0.1 ppm Fe, 300 ppm HDO, and 20 ppm D2O?

I say yes. What say you?

I looks like we both have an uneasiness with possible world semantics. I think your unease is more with the metaphysics, while mine is with the application. The PI sections you had mentions, 253 to 256 are typically associated with Wittgenstein's argument around private language. Should this extend to possible world semantics? At first glance, I would say "no". Possible worlds are not suppose to be a private language. In PI, a private language is about language only a single individual understands that refers to purely private inner experiences.

So Kripke just makes a deceptive use of language, to produce the appearance that the table in his hands could also be in another room. — Metaphysician Undercover

He does not say this in the quote I mentioned from N&N. What he says is "Don't ask: how can I identify this table in another possible world, except by its properties? I have the table in my hands, I can point to it, and when I ask whether it might have been in another room, I am talking, by definition, about it."

He is not saying if the table in my hands is also in another room, but whether it might have been in another room. And, he is talking, by definition, about it.

I have no issue with this plain speak. We use this kind of language all of the time in real life. We sit down with old friends, talk about old times and reminisce about "might have beens."

But sometimes philosophers should live well enough only. In this case, they go and introduce the concept of "possible world". My intuition tells me just because you can imagine something does not mean it is possible. And when I use the word "possible", I mean it in the most general sense. Also, alternatively, just because you can't imagine something does not mean it is impossible. For instance, we have learned that nothing can go faster than the speed of light. But some would like to qualify this and say "This is a physically impossible, but not metaphysically or logically." Yet, these limits were not derive from experiments, but are derived conceptually. While one can imagine numbers greater than the speed of light without contradiction, those numbers conceptually would quickly undermine our notions of time, space, and causality, basically reality itself would become unintelligible.

Let's

I can conceive some gold is Au if fool’s gold gets $4500 oz. Do I need guidance from possible world semantics to clarify that my use of “some” needs correction? — Richard B

Semantics in general, can be understood as situationally defining types, e.g the natural kind gold, in terms of a set of tests, where a failure to pass any of the tests implies the negation of the type, e.g. if this nugget fails to pass the tests of heaviness, malleability and yellowness, then by definition this nugget is not "Gold", i.e. it is of type "Not-Gold". So we have a de dicto component, namely the set of tests that we use to situationally define the type "Not-Gold", and a de re component, namely whether or not our nugget passes or fails ours tests.

Strictly speaking, since natural kinds, indeed any physical kind, are not exhaustively defineable on the one hand, and yet we can only specify finite sets of tests and make finite observations on the other, we should only conclude that something is of type "Not-X" in line with Popper's principle of falsification. E.g we should define "Gold" to be "Not-Not-Gold" whose meaning is situational and in relation to a finite set of tests that we using situationally to define and test for "Not-Gold" (softness, brittleness, etc).

This points towards local definitions for natural kinds that lose their transcendental significance; for different sets of tests will be used in different contexts. e.g although gold has a unique spectral "fingerprint" that can be observed using techniques like X-ray Fluorescence, in most situations such techniques aren't available and hence are not included in the tests that are used to situationally define the presence of "gold". But even when such techniques are available, perhaps the spectrometer is broken, fraud takes place, new scientific laws pop into existence etc. So tests themselves require higher-order tests (i.e. "necessity" is contigent and loses epistemological significance).

We can now think of rigid-designation as a harmless and comedic truism which says that "if" we could non-situationally define gold, by exhaustively specifying what "gold" is in terms of an infinite number of infallible tests covering all contexts and use cases, and "if" our purported sample of 'gold' passed every one of those tests, then we would necessarily "have gold" de dicto, in accordance with our definitions of "gold" and first-order "necessity".

This brings us to the "possible world" variety of semantics: we can think of the execution of a test as updating the state of our world, which is modelled in possible world semantics as a transition to another world. Tests reinforce the idea that the accessibility relation used in in possible world semantics expresses a non-deterministic version of causal implication in relation to a set of non-deterministic causal assumptions. When possible world semantics goes wrong or is under-constrained, it is because the underlying causal assumptions are wrong or under-constrained.

I looks like we both have an uneasiness with possible world semantics. I think your unease is more with the metaphysics, while mine is with the application. The PI sections you had mentions, 253 to 256 are typically associated with Wittgenstein's argument around private language. Should this extend to possible world semantics? At first glance, I would say "no". Possible worlds are not suppose to be a private language. In PI, a private language is about language only a single individual understands that refers to purely private inner experiences. — Richard B

The issue is the relationship between one possible world and another, and the discontinuity implied by that relationship. If someone assumes that there is an object with the same identity in multiple possible worlds, then this supposed object is nothing but an object of a private language, unless the continuity between distinct possible worlds can be established. So it's not that possible worlds are supposed to be a private language, but that the matter of transworld identity creates a private language problem. The matter is the problem of identifying objects which exist in distinct mental images, as "the same object". That is the private language problem. The assumption of "the same" is unjustified, rendering the proposed "object" being an unity of multiple instantiations, as unintelligible.

Think about the chair in Wittgenstein's example. Suppose I insist that the chair here today is the same chair that was here yesterday. This is analogous to saying that the thing named "Nixon" in one possible world is the same as the thing name "Nixon" in another possible world. So you may ask me to justify my claim that the chair is the same object. Since it is a publicly accessible object, I could say look at it, doesn't it look exactly the same. It's identical. That still might not appease you, because you could say that every room in the building has identical chairs, how do I know that they weren't switched. Then, I could say that someone watched over it in the interim, or refer to security video, and the continuity required to justify my claim could be justified.

In the case of "Nixon", justification cannot be done in the same way because the possible worlds are inner objects, imaginary. This means that the continuity of the proposed object referred to, between distinct possible worlds, must also be imaginary, fictitious, or stipulated. And if the thing referred to as "Nixon", is supposed to be the same thing in multiple possible worlds, this stipulation needs to be justified. What makes it "the same thing"? Obviously it's not identical because the different worlds give it different properties. And the supposed continuity from one possible world to the next is not a temporal continuity, so reference to observation, or surveillance is not relevant. Nevertheless, we need justification. Without justification it is simply a private object which is absolutely unintelligible.

In Wittgenstein's other example, where "S" signifies a private thing referred to as "a sensation", the thing referred to is unintelligible to others, until justification of the use of "S" is provided. It turns out that the use of "S" coincides with an observable rise in blood pressure, and this forms the justification. That could be the "essential property" of the sensation referred to by "S". Now justification of continuity between distinct worlds could be done through an essential or necessary property. We could do the same with the thing referred to by "Nixon". We could say that there are essential, or necessary properties, which identify the thing called "Nixon", in every possible world, and this would suffice for transworld identity. However, notice how this arbitrarily, or subjectively, limits the extent of possibility. The number of possible worlds is thereby limited. This amounts to saying that it is impossible for there to be a possible world where the thing called "Nixon" does not have the named essential properties. Therefore the limiting of the possibilities in this way, itself need to be justified. And the choice of these limiting factors becomes very subjective dependent on purpose. And if we want to allow all possibilities, infinite possibility, we must deny any essential properties, and we are back at an unjustifiable, and completely unintelligible object of a private language.

If you take a look at the SEP's description of combinatorialism, the issue might become more clear to you. Here, the object of the private language is called the "simple". The simple has transworld identity as such, having no essential properties, allowing for infinite possibilities. However, because it has no inherent properties it is completely unintelligible, as an object of a private language. Being a private language doesn't mean that we cannot use the word, it just means that what the word refers to cannot be known. So we can all talk about "the simple", just like we can all talk about "the beetle", but this talk doesn't make the private object referred to, intelligible.

So you'll notice in the SEP, that the different philosophers who use this system, of employing "the simple", have different ideas of what "the simple" refers to. That is because it is essentially an object of a private language, in a case where justification of the use of the term varies according to an individual's preference, or purpose. In general, "the simple" is supposed to be an object whose identity, and existence, cannot be justified, as simply a requirement for unlimited possibility. This leaves justification as completely subjective, because justification is to apply limits, boundaries. Consequently the philosopher is allowed to apply limits, and justify what "the simple" refers to, according to the purpose at hand. But the object of the private language is inherently unbounded and therefore unintelligible, then the philosopher applies limits as desired. However, the application of boundaries. limits, is contrary to the basic assumption, and need within the system. The need is for an unlimited object of the private language, and the corresponding assumption. so we are left with self-contradiction when we try to make the object of the private language, referred to here as "the simple", into something which could be understood.

Reading the SEP, you'll see that the simple has a different meaning for Russell as it does for Wittgenstein. Also Quine and Cresswell suggest a different interpretation. Armstrong argues something different. Ultimately, the ontology of "the simple" is a matter of debate. This is because it is employed as the object of a private language, whose existence cannot be justified. That is the purpose of "the simple", to allow for transworld relations which cannot be justified. And, as the object of a private language use of the term is completely unjustifiable. Attempts at justification are self defeating

He does not say this in the quote I mentioned from N&N. What he says is "Don't ask: how can I identify this table in another possible world, except by its properties? I have the table in my hands, I can point to it, and when I ask whether it might have been in another room, I am talking, by definition, about it." — Richard B

Look at what he is saying Richard B. The table being spoken about is referred to as the one "I can point to", "the table in my hands". That is very clearly how "the table" is defined here, in this context, by Kripke. It is impossible that this table, the one indicated by the definition, as the one "I can point to", "the table in my hands", could be in another room, or else it would not be the defined table.

Therefore his question is answered very easily. He cannot identify this table in another possible world. That is because he has defined the table spoken about as the table here, and now, in this world, the table I can point to, the table in my hands. By defining the proposed object in this way, he denies the possibility that it could be in another possible world.