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This question arose from the discussion of my recent question, [When is the first appearance of Phosphorus after March 21, 2021?][1] One of the other arguments in Kripke's 'Naming and Necessity' is that water is necessarily H2O, as 'water' and 'H2O' are rigid designators of the same thing.

Obviously (I think!), this argument must work equivalently for 'ice is necessarily H2O' and 'steam is necessarily H2O', and thus (perhaps less obviously, from the transitivity of identity) 'steam is necessarily ice'.

With regard to my earlier question, it was suggested that there is merely some ambiguity in ordinary usage, but I do not see any such ambiguity, either there or here: when someone says 'steam', we would not ordinarily wonder if they meant 'ice', and vice-versa. On the other hand, if they are metaphysically necessarily identical, why would it even be possible to be confused if someone freely mixed up the use of 'ice' and 'steam'? There may be a clue to resolving this in Frege's second puzzle, but it is not clear to me that the specific resolution there, in terms of the usage being in the context of propositional attitudes, generalizes to all uses of 'steam' and 'ice'.

So, if steam is necessarily ice, how does one resolve the apparent paradox of identity? And if not, where did I go wrong in concluding that it is?

Addendum:

The responses that I have received so far show that I should have been clearer in phrasing the question, which is not to argue for a seemingly nonsensical position, but is about what seems to me to be a paradox arising from a pair of Kripke's examples of a posteriori necessity: if you substitute "steam" for "Hesperus", "ice" for "Phosphorus", and "H2O" for "Venus" in Kripke's "Hesperus is necessarily Phosphorus" argument, you get an argument for the conclusion "steam is necessarily ice".

One may, of course, challenge this substitution, but I think there are grounds for accepting it. Another of Kripke's examples is that water is necessarily H2O, from "water" being a rigid designator of "H2O". It seems to me that both "steam" and "ice" are equally rigid designators of "H2O". They apparently fit the SEP definition: "A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else" - disambiguating, if someone feels the need, by saying "water ice" and "water steam" - or, at least, they fit the definition as least as well as do Hesperus and Phosphorus with regard to rigidly designating Venus; ice is not just H2O, but neither is Hesperus just Venus, and H2O is not always ice, but neither is Venus always Hesperus, and the above definition of "rigid designator" does not require them to be so, anyway. In neither the Hesperus / Venus case nor the ice / water case do we have a simple synonym, such as in another of Kripke's examples, Cicero / Tully.

  [1]: When is the first appearance of Phosphorus after March 21, 2021?

A Raybould
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  • Your mistake is applying the identity relationship to "ice", "steam", "water", and "H20". – curiousdannii Oct 17 '20 at 14:33
  • @curiousdannii As far as I know, I am just following Kripke's argument here. Perhaps you could post an answer explaining in more detail where we are going wrong. – A Raybould Oct 17 '20 at 15:11
  • why not post this on the physics stack exchange? – niels nielsen Oct 17 '20 at 16:13
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    Ice is H2O in solid state, and steam is H2O in gaseous state, so neither is H2O *simpliciter* and necessarily (or even actually) the other. The correct versions will be "the material of ice is necessarily H2O", "the material of steam is necessarily H2O", and "the material of steam is necessarily the material of ice". While "water" is used ambiguously to refer to both a chemical material *simpliciter* and its liquid state, "steam" and "ice" are not. *If* they are then "steam is necessarily ice" is true on that disambiguation. – Conifold Oct 17 '20 at 17:36
  • @ARaybould I couldn't see where to read Kripke's argument. If he does use the word "identity" to relate these words you should [edit] this question to add quotes showing how he reasons. – curiousdannii Oct 17 '20 at 23:44
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    @Conifold Your answer is spot on. Since niels nielsen's answer misses the point entirely, why don't you post your response as an answer so I can upvote it? – Bumble Oct 18 '20 at 03:47

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Ice is H2O in solid state, and steam is H2O in gaseous state, so neither is H2O simpliciter and necessarily (or even actually) the other. The correct versions will be "the material of ice is necessarily H2O", "the material of steam is necessarily H2O", and "the material of steam is necessarily the material of ice". While "water" is used ambiguously to refer to both a chemical material simpliciter and its liquid state, "steam" and "ice" are not. If they are then "steam is necessarily ice" is true on that disambiguation.

To make it even more pronounced, "lead is necessarily matter", "gold is necessarily matter", but lead is not gold, even though it can be transmuted into gold by a nuclear reaction. Many nouns refer more specifically than to the very base material, and sometimes are ambiguous, i.e. specificity depends on context.

The situation occurs even with proper names, like Hesperus and Phosphorus, that "officially" are supposed to refer to the unique underlying object. It is in this sense that "Hesperus is necessarily Phosphorus". But this is not necessarily how they function in common usage. In some contexts Phosphorus may well function as synonymous to what Russell calls a definite description, "the morning star" being its abbreviation. It stands for the appearances of Venus in the morning, while Hesperus for its appearances in the evening. If so, Hesperus is not Phosphorus, they describe different groups of events.

Conifold
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  • I have no disagreement with what you have written here, but it is still not clear to me that there is a consistent way in which Hesperus is a rigid designator of the planet Venus, while ice is not a rigid designator of the compound H2O - after all, they both designate the same object in all possible worlds in which that object exists and never designate anything else, and neither are simple synonyms (and if H2O is not an object in this sense, then water itself is not a rigid designator of H2O)... My apologies if I seem to be moving the goalposts; I can make this a separate question. – A Raybould Oct 18 '20 at 21:03
  • @ARaybould Ice is a natural kind in Kripke's theory, Hesperus is a proper name, so they are dissimilar to begin with. The adherence to rigid designation in everyday use is much stronger for proper names than for kinds. And while ice is a rigid designator (let's say) it is not a designator of H2O, its kind is more specific and includes phase state in addition to chemical composition. Just as lead and gold are different kinds so are ice and steam. The "is" in "X is Y" is not always used for identity, it is also used for non-reversible subsumption, as it is in "ice is water" or "gold is metal". – Conifold Oct 19 '20 at 07:21
  • This still seems inconsistent to me. While ice designates something more specific than just H2O, surely Hesperus also designates something more specific than just Venus - it designates Venus in a specific spatial relationship (which itself is physical state) to the Earth-Sun system (in fact, are you not suggesting as much in your answer?) Also, Kripke specifically accepts natural kinds as strict designators (the "water is necessarily H20 argument" depends on it, of course), so the difference in these cases cannot simply be that ice is a natural kind, not a name, either. – A Raybould Oct 19 '20 at 22:21
  • On the other hand, the [SEP entry](https://plato.stanford.edu/entries/rigid-designators/) is so noncommittal over what, exactly, counts a a rigid designator that, while I am not persuaded that there is nothing to see here, I can see that your view is well within the range of philosophical positions on the issue. – A Raybould Oct 19 '20 at 22:30
  • @ARaybould I do not think rigid designation plays any role in this question. Kripke does accept that names and kinds refer rigidly, but that is moot in deciding *what* they refer to. The reference of ice or Hesperus is what decides the question already in the actual world, whether it extends rigidly or not to other possible worlds is only responsible for inserting "necessarily". Does "Hesperus" refer to planet Venus and nothing more specific? In "Hesperus is Phosphorus" it does. Does "ice" *ever* refer to H2O only? I doubt it. But that's on common usage, not on Kripke's rigidity status. – Conifold Oct 20 '20 at 00:34
  • As you say, "whether it extends rigidly or not to other possible worlds is only responsible for inserting 'necessarily'",  and indeed, the question is not "is steam ice" but "is steam _necessarily_ ice", because the paradox (if there is one) arises from Kripke's examples of a posteriori necessity, in which rigid designation is key, and also the route to the paradox does not go through  a premise or lemma that "steam is ice" in the actual world (see also my clarification of the question.) For the same 'source of the paradox' reason, common usage is not an issue... – A Raybould Oct 20 '20 at 20:39
  • If we are limiting scope to what's being designated just within these arguments, I can equally say that in "steam is necessarily ice", "ice" refers only to H2O - its state is no more an issue than is Venus' position in "Hesperus is Phosphorus"... – A Raybould Oct 20 '20 at 20:45
  • Also, if, in "Hesperus is Phosphorus", Hesperus and Phosphorus are not taken to be _identical_ with Venus, conforming to Leibniz's law that if a = b then anything true of a is true of b (and vice-versa, by its symmetry), then I do not think we can get to the identity of Hesperus and Phosphorus, and without that, the Barcan-Kripke proof that identity is a necessary truth, which is predicated on Leibnitz's law, cannot be used to establish the necessity of Hesperus being Phosphorus - and for the reasons I gave before, there are ways I think these putative identities fail the Leibnitz test. – A Raybould Oct 20 '20 at 20:46
  • @ARaybould On my understanding, Kripke's theory does not decide when X is Y, it only says that *if* X is Y, and X,Y are names or natural kinds, *then* we can insert "necessarily" (keeping the sense of "X", "Y" and "is" the same). So "X is Y" *is* a required lemma. Thus, water is necessarily H2O, gold is necessarily metal, but ice is not steam, and so ice is necessarily not steam. If phase state is not an issue for you and steam is ice then steam is necessarily ice, but there is no paradox. If Hesperus is not Phosphorus for you then it is not so necessarily all the more. Common usage decides. – Conifold Oct 20 '20 at 21:34
  • The argument here is explicitly just a substitution of terms into Kripke's "Hesperus is necessarily Phosphorus" argument, so if "steam is ice" is a lemma here, then "Hesperus is Phosphorus" is a lemma in Kripke's argument, but it is not - the 'X is Y's in that argument are that Hesperus is Venus and Phosphorus is Venus, leading (by the identity of two things that are identical to the same) to the _conclusion_ that Hesperus is necessarily Phosphorus" (which has, as a _corollary_, that Hesperus is Phosphorus in the actual world). So, what does common usage decide about "ice is H2O"?. – A Raybould Oct 21 '20 at 11:58
  • @ARaybould Unfolding X is Y into X is Z and Y is Z does not change much as long as "is" means identity. Common usage decides that it does not in "ice is water", while it does in "Hesperus is Venus". Kripke's argument would not work for "canines are necessarily felines" either even though both are mammals, for the same reason. Surely it is not anything about rigid designation that makes us use "ice is water" the same way as "felines are mammals", and not the same way as "felines are cats" (in the broad sense of "cat"). Just because terms designate rigidly does not mean "is" stands for identity. – Conifold Oct 21 '20 at 12:25
  • I do not have time right now for a full response, but two quick points: Firstly, I disagree about unfolding the argument: it is in that form because it would not be valid (or, at least, vacuous) otherwise. If you take the conclusion and make it a lemma, you are begging the question (incidentally, this has been said of Kripke's arguments, I believe). Secondly, you have mentioned a great many identity propositions, _except_ "ice is H2O". I assume you accept that common usage has decided that this is a true proposition. – A Raybould Oct 21 '20 at 13:04
  • @ARaybould I used "water" and "H2O" interchangeably. If "is" stands for identity "H2O is not ice" is true, and "ice is H2O" false. It is true only with "is" for subsumption, entirely analogous to "felines are mammals" or "gold is metal". With "is" for identity replacing "X is Z and Y is Z" by "X is Y" has no effect on validity or vacuity, but with "is" for subsumption it is invalid. This is why "ice is steam" is false, but "water is H2O" true. And this is why we can not take two random kind terms and equate them as in "gold is necessarily water", while we can always find a common Z term. – Conifold Oct 21 '20 at 13:33
  • So here we have what looks like a straightforward proposition, 'ice is H2O' (superficially so much like 'water is H2O'), and I would wager that, according to common usage (which is, we are told, decisive), a solid majority of those who know the facts of the matter would consider this a true proposition. Your analysis shows, however, that it has no definite truth value as it stands, as it could be taken as either true or false depending on how it is disambiguated... – A Raybould Oct 22 '20 at 23:53
  • Does philosophy generally hold that ambiguous sentences cannot be propositions, or perhaps that ambiguous propositions do not have definite truth values? I think either way could work, though I suspect it is the former, as this would be consistent with what I understand logic's position to be, which is that ambiguous sentences cannot be well-formed propositions. Regardless, it seems to me that some clear way of dealing with ambiguous would-be propositions is required. – A Raybould Oct 22 '20 at 23:56
  • @ARaybould I think they consider it (unconditionally) true only because they reflexively disambiguate from (perceived) context, which is how mind tends to operate, or by habit from prior such exercises. Once ice-water/gold-metal analogy is pointed out they are likely to acknowledge the ambiguity. I think the traditional position is that formal statements must be unambiguous, and ambiguous formulas are a syntax error, hence official warnings about "abuse of notation" in informal mathematical texts. And yet said abuse is pervasive, it must play some vital function in natural language. – Conifold Oct 23 '20 at 04:34
  • Large part of it is economy of language, I reckon. A feature is that ambiguity is typically limited, it is often (but not always) possible to extract 2-3 coherent formalizable meanings, as with the copula, and so why waste memory on multiple words when context/elaboration distinguish them well enough in concrete uses. The situation is different for vague terms, with a continuous spectrum of ambiguity, but that too has its own useful functions, distinct from economy. It allows making informative true statements when no precise true statement can be made for lack of knowledge. – Conifold Oct 23 '20 at 04:44
  • If we start by putting aside necessity, there are straightforward disambiguations of 'is' that we can all agree on: 'water', 'steam' and 'ice' all refer to the same substance, and 'Venus', 'Phosphorus' and 'Hesperus' all refer to the same planet. But what about the necessity of these relationships? – A Raybould Oct 24 '20 at 02:21
  • In the case of water and H2O, the identity reading of 'is' is also correct, and we can apply the Barcan-Kripke theorem to establish the necessity of this reading of 'is'. This only works for the identity reading, however, not the same-substance reading, because the theorem depends on Liebnitz's law. As you point out, the identity reading of 'is' is not correct in the case of "steam is necessarily ice", so the Barcan-Kripke theorem cannot be used to yield "steam is necessarily ice". Note that this is so even though we may well think that steam is necesarily the same substance as ice. – A Raybould Oct 24 '20 at 02:22
  • What I am suggesting here is that the identity reading of 'is' does not work for Hesperus and Phosphorus either, as they fail the Liebnitz test in cases like "when is V next visible?",  where you get a different answer when V is Phosphorus than when V is Hesperus. The situation seems to be an almost-exact parallel of the steam/ice case. Russell, for one, has held that Hesperus and Phosphorus are not really purely referential names. – A Raybould Oct 24 '20 at 02:22
  • So now I am wondering if rigid designation is a sort of sufficiently-similar relationship that can be substituted into the Barcan-Kripke theorem to yield necessity where the two things or kinds are merely similar in certain ways (e.g. same planet or substance.) As I noted earlier, the SEP definition of 'rigid designator' accepts both steam and ice as rigid designators of H2O, which is not what we want; tacking "...and vice-versa" on the end of that definition would fix these two cases, but I do not know if this is the right way to go about it... – A Raybould Oct 24 '20 at 02:23
  • @ARaybould Kripke's response is that all is fine with identity "is", but the Leibniz's law fails in intensional contexts, which is what "when is V next visible?" is interpreted as to get different answers. Russell, of course, held that Hesperus and Phosphorus are definite descriptions. The controversy between descriptivism and Millianism is ongoing, both cite competing linguistic intuitions, and, truth be told, there is probably a mixture of both uses in common talk, to the chagrin of purists. – Conifold Oct 24 '20 at 10:44
  • I suspect that any attempt to find an entirely consistent set of laws governing common talk (aka language, as I take laguage to be that which people actually speak) is doomed to failure... I take your point with respect to Liebnitz's law and intensional contexts, but if one holds that Phosphorus is identical with Venus, are you not logically obliged to regard the 'next appearance of Phosphorus' question in an extensional context? Even if not, there seems to be an issue here that goes away if you disambiguate 'is', in "Phosphorus is Venus", as "is the same planet" rather than as identity. – A Raybould Oct 24 '20 at 22:59
  • @ARaybould Millians still have to explain *why* Lebniz's law fails and when they do the result looks much like a rephrasing of descriptivism, with "guises" in place of Frege's senses, as Forbes pointed out in his [review of Salmon's Frege's Puzzle](https://www.jstor.org/stable/2185233). Your example is interesting in that there is no recognition failure as in "Clark Kent can fly", the speaker is presumably aware of Venus's "guises". But I think they have a response along the same lines. – Conifold Oct 25 '20 at 04:21
  • When P is used instead of V in an observational context there is a strong clue of a context shift to intensional reading, in full agreement with Grice's maxim of relevance, otherwise why not just ask it with V. And if the shift is explicitly overridden, e.g. by adding "and I use P and V interchangeably", then the issue is resolved. You could say that if P always triggers a context shift then something is wrong with "is" in "P is V", and they will say that semantics is distinct from pragmatics, and it does not do so always, e.g. not in clear *de re* contexts like "P/V has a thick atmosphere". – Conifold Oct 25 '20 at 04:32
  • In other words, differences in perlocutionary force, such as P's ability to shift context, do not amount to differences in semantic meaning, reflected in "is". I suppose one could massage rigid designation, and some Millians came up with variations on it, but its real purpose is to interpret counterfactuals and explain how possible worlds underlying them are "constructed", and your example is not that. – Conifold Oct 25 '20 at 04:41
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/115496/discussion-between-a-raybould-and-conifold). – A Raybould Oct 25 '20 at 13:41
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Before we get technical about what the term “identical” means, we should get technical about two more elementary words in the OP question: “steam” isn’t necessarily composed of dihydrogen monoxide. Merriam-Webster defines it as “a vapor arising from a heated substance”: https://www.merriam-webster.com/dictionary/steam

Similarly, “ice” might not be composed of H2O per se at the molecular level. Cf. again Merriam-Webster, which mentions “ammonia ice” in one of its definitions: https://www.merriam-webster.com/dictionary/ice

So as posed in the form “Is steam necessarily ice?” the answer to the OP’s question is “no” on the basis not just of states of matter but of molecular composition, since the steam of one compound would be different in both senses from the ice of another.

Rivers McForge
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  • Thank you for your response. You are right, but I do not think this lexical approach can deal with the issues these examples are intended to demonstrate - after all, in English, phosphorus (used by Kripke in an analogous argument) is not just the morning star, but also element #15. I think all these issues could be fixed by being pedantically unambiguous - e.g. by saying 'water ice' and 'water steam' - but context seems to be sufficient disambiguation here. – A Raybould Oct 18 '20 at 21:13
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Might it be useful to talk about the Type/Token distinction here?

Basically, when you talk about Hesperus or Phosphorus, you talk about one or more Token individuals. When you talk about Water or Ice, you talk about a class or type of thing, more than you do any one specific individual instance of it.

Token-Token identity and Type-Type identity function rather differently in modal contexts. When we talk about the trans-world identity of Tokens, we are asking if this one object is the same across multiple modalities. When we talk about the identity of Types, we are talking about something more like “Are all tokens of type A (in this/in all modalities) also tokens of type B?” - (depending on our theory of types it might well be true that our types are the same abstract logical object, but this is not really what we’re asking about in type/type identity!)

Sofie Selnes
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  • That is a fair question, but as Kripke has already "crossed the line" in his "water is necessarily H2O" argument, I think one would have to argue that ice is different than water in this respect. – A Raybould Oct 21 '20 at 12:14
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This seems to me to be a nonissue in the sense that Kripke wasn't a physicist, a mathematician or a physical chemist. In those fields there are no nomenclature controversies whatsoever regarding the phase diagram for H2O or the kinetic processes by which phase transformations occur. In other words, trained practitioners in those fields have no trouble accepting the idea that one molecule can exist in three different phases (solid, liquid, and gas) and no one splits hairs and/or loses sleep about whether or not it is correct to call ice "steam": ice is ice, water is water, and steam is steam, and at the same time, solid water is ice, liquid water is water, and water vapor is steam.

niels nielsen
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  • There does not seem to be any confusion over what the facts of these matters are in the actual world, but the issue in Kripke's examples is the metaphysical question of what must be necessarily so, as opposed to being contingent on how the actual world is. In my reply to Conifold, you can see what I still don't get about these examples. – A Raybould Oct 19 '20 at 00:43
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    I am glad to be a recovering ex-engineer rather than a philosopher! – niels nielsen Oct 19 '20 at 02:17
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This muddle arises from the two meanings of "be"/"is". One meaning: An "identity" -- if Thing A is Thing B then they are identical and interchangeable. The other meaning: An "instance of", or "member of the set": If Thing A is a Thing B then it has the characteristics that have been assigned to the class of objects/concepts known as Thing B.

In practice the "identity" meaning rarely applies, but its application does occur more commonly in formal math and formal logic.

(And it is amazingly hard to figure out how to word the above without using "is".)

Hot Licks
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  • Ah - the Clintonian Conundrum over the meaning of 'is'! For the purposes of this question, this becomes the issue of what counts as a '[rigid designator](https://plato.stanford.edu/entries/rigid-designators/)'. – A Raybould Oct 19 '20 at 00:51
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Is seawater, water? This proved a true & lasting problem in architectural research, where the method for Roman concrete was thought in the various places it was found to be recorded, to be missing some secret ingredient. It turned out they used seawater instead of freshwater, and were able to create harbour walls that in some cases have survived about 2 millenia, much better than our modern concretes up until this discovery had been able to survive in the sea.

What about the triple point of water, where liquid solid and gaseous water all coexist? How could you say anything but H20 is steam & ice, at that combination of pressure & temperature, hovering exactly between having three phases & only two (so able to sublime, not just melt)?

"In this sort of predicament, always ask yourself: How did we learn the meaning of this word ("good", for instance)? From what sort of examples? In what language-games? Then it will be easier for you to see that the word must have a family of meanings." -Wittgenstein, in Philosophical Investigations

Necessarily identical? That can only be meaningful, nested within a context of definitions, of language in use. Our definition of water, of solution, impurities, elemental atomic constituents, temperature & pressure conditions, obviously cannot apply to the writings of Ancient Rome!

generalizes to all uses of 'steam' and 'ice'

Why would it? We use examples to build our network of definitions, and they change & refine - & will continue to do so. Just as logic seeks to reduce axioms or assumptions without losing scope, so in science, and with atomic theory a huge range of behaviours can be predicted without seeing them, and like that we reduce what is contingent. Science has got down to 26 constants + the initial conditions, away from a fully self-consistent picture - a fracture plane of the E8 hypercrystal might reduce this to just initial conditions, or closer too.

The best or most accurate definition, only integrates with the largest self-coherent system, ie science (for now - perhaps in the future, some 'glass bead game').

Yet, when Blake says:

"I was angry with my foe: I told it not, my wrath did grow. And I waterd it in fears, Night & morning with my tears"

That is still part of our understanding of water, using it as a metaphor of what we cultivate, how we use our attention, based on familiar cases/examples, with 'family resemblances'. This is another kind of language, which can bring emotional depth with 'fluid' metaphors. It won't be subsumed by science, only remain part of a less integrated and consistent domain of language, which we are perfectly happy to code-switch to, knowing the different kinds of implications being made.

Mathematics and logic occurs within the domain of definitions, of settled constants, and can only be used there. There is no transcendent place to declare the truest definitions from, only the best integrated intersubjective space.

CriglCragl
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  • Note that if your seawater case is an effective objection here, it would also be an effective objection to Kripke's "water is necessarily H2O" argument... More generally, I think all these informal arguments should be tacitly read, i.e. as if the obviously-intended disambiguations and caveats had been made, or else they would be almost unreadable. Of course, these should all be _uncontroversial_ tacit readings of the text, and applicable in the specific context of the argument. They should also be applied consistently, which is one issue in my discussion with @Conifold. – A Raybould Oct 21 '20 at 12:27
  • "They should also be applied consistently" They should be applied contextually. – CriglCragl Oct 21 '20 at 21:09