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?


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?

  • Your mistake is applying the identity relationship to "ice", "steam", "water", and "H20". Commented Oct 17, 2020 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
    Commented Oct 17, 2020 at 15:11
  • why not post this on the physics stack exchange? Commented Oct 17, 2020 at 16:13
  • 5
    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
    Commented Oct 17, 2020 at 17:36
  • 1
    @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
    Commented Oct 18, 2020 at 3:47

6 Answers 6


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.

  • 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
    Commented Oct 18, 2020 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
    Commented Oct 19, 2020 at 7:21
  • 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
    Commented Oct 19, 2020 at 22:21
  • On the other hand, the SEP entry 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
    Commented Oct 19, 2020 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
    Commented Oct 20, 2020 at 0:34

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.

  • 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
    Commented Oct 18, 2020 at 21:13

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!)

  • 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
    Commented Oct 21, 2020 at 12:14

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.

  • 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
    Commented Oct 19, 2020 at 0:43
  • 1
    I am glad to be a recovering ex-engineer rather than a philosopher! Commented Oct 19, 2020 at 2:17

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".)

  • 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'.
    – A Raybould
    Commented Oct 19, 2020 at 0:51

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.

  • 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
    Commented Oct 21, 2020 at 12:27
  • "They should also be applied consistently" They should be applied contextually.
    – CriglCragl
    Commented Oct 21, 2020 at 21:09

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .