Necessity and Metaphysics

What is it for something to be necessary — and why should a claim about how things must be count as a claim about the world rather than about our language or our concepts? This remark takes up the modal notions that modern metaphysics runs on, starting from the two pieces of background everything else depends on: Kripke's Naming and Necessity, which made de re modality respectable again, and the notion of metaphysical necessity that it left in place. It then presses a worry about the workhorse example: water is ${\mathrm{H}}_2\mathrm{O}$ is ambiguous between a claim about molecules and a claim about a substance, and once the readings are separated, the necessity turns out to rest on an essentialist premise that the chemistry does not supply. The companion example, gold is the element with atomic number 79, raises the complementary worry: there the criterion is supplied by the science itself, which makes the necessity look like a fact about a classificatory scheme rather than about the metal. Both defences run through the claim that the necessity is de re — about the stuff, not the word — so the remark asks how much of a theory of reference that defence has to presuppose, and closes on Hesperus is Phosphorus, the case usually held to be immune, where a third ambiguity lurks and the question of framework-relativity can be posed in its sharpest form — ending with the historical version of the deflation, which asks whether the empirical discovery of a necessity is just the formation and entrenchment of a convention seen from inside, and then with the question of whether the two camps are separated by anything more than notation — closing with a balance sheet of what each side leaves unexplained.

The technical treatment lives in Possibility and Necessity, Possible Worlds, and Modality and Essence; the semantic background is in Semantics and the Theory of Meaning.

Background: Naming and Necessity

Kripke's 1970 lectures (published 1980) did two things at once: they replaced the reigning theory of how proper names refer, and they used the replacement to pull apart three distinctions that had been run together for half a century.

Against descriptivism. On the Frege–Russell view, refined by Searle into a "cluster" theory, a name is semantically equivalent to a description or family of descriptions the speaker associates with it: "Gödel" means the man who proved the incompleteness of arithmetic. Kripke's objections are famous and largely decisive:

• The modal argument. "Gödel might not have proved incompleteness" is plainly true, but on the description theory it says that the man who proved incompleteness might not have proved incompleteness. The name and the description behave differently under $\square$ and $◊$, so they are not synonymous.
• The epistemic argument. If the name meant the description, "Gödel proved incompleteness" would be knowable a priori. It is not.
• The semantic argument. Suppose the theorem was actually proved by a man named Schmidt, from whom Gödel stole it. Then "Gödel" in our mouths still refers to Gödel — the thief — not to whoever satisfies the description. Reference can survive massive error.

Rigid designation. A term is a rigid designator if it picks out the same object in every possible world in which that object exists. Proper names are rigid; most definite descriptions ("the inventor of the bifocals") are not. This single notion carries the modal argument: an identity flanked by two rigid designators, if true, cannot be contingently true, so Hesperus is Phosphorus holds in every world — even though it took astronomy to discover it. The same treatment extends to natural-kind terms: "water," "gold," "heat" rigidly designate kinds whose underlying nature is discovered empirically, so water is ${\mathrm{H}}_2\mathrm{O}$ is likewise necessary and a posteriori.

The causal–historical picture. If descriptions do not fix reference, what does? Kripke offers not a theory but a picture: an initial baptism attaches the name to an object, and subsequent uses refer to it by way of a causal chain of communication, each speaker intending to use the name as received. Speakers need know almost nothing about the referent; the linguistic community does the work. Putnam's parallel argument for kind terms — the Twin Earth cases and the division of linguistic labour — makes the same externalist point: meaning "ain't in the head."

The three distinctions. The philosophical payload is the separation of what the logical positivists had treated as one distinction under three names:

Once these come apart, both off-diagonal cases are live. The necessary a posteriori (Hesperus is Phosphorus, water is ${\mathrm{H}}_2\mathrm{O}$, this table is made of this wood) is the important one: we discover empirically which object or kind we were referring to, and the necessity then follows from the necessity of identity together with rigidity. The contingent a priori (the standard metre bar) is the mirror image: a description may fix the reference of a term without giving its meaning, and what is stipulated is then known a priori but could have been otherwise.

Why it mattered. Quine had argued that quantifying into modal contexts — hence essentialism — was unintelligible, and the positivists had reduced all necessity to analyticity. Kripke's cases exhibit necessities that are neither analytic nor knowable a priori, which means necessity cannot be explained away as a shadow of our conventions. Modality is thereby returned to the world, and de re modal predication — an object's having a property necessarily, independently of how it is described — is back on the table. That is what re-opened analytic metaphysics.

Background: metaphysical necessity

Metaphysical necessity is truth in all possible worlds simpliciter — necessity flowing from the natures of things rather than from logic, meaning, convention, or physical law. It is the modality the ontologist cares about, and its distinctive feature is being broader than logical necessity in what it rules out, but narrower than nomological necessity in what it permits.

Its place among the modalities. Compare across the standard flavours:

• Not logical necessity. "Water is not ${\mathrm{H}}_2\mathrm{O}$" is logically consistent and violates no formal law, yet is metaphysically impossible.
• Not conceptual or analytic necessity. The concept water does not contain ${\mathrm{H}}_2\mathrm{O}$; competent speakers used the word for millennia without the chemistry. So the necessity is not underwritten by meaning.
• Not nomological necessity. Metaphysical possibility is strictly wider: the laws of nature could have been otherwise, so worlds with different laws are metaphysically possible though nomologically impossible.

Nesting the boxes: the metaphysically necessary includes the logically and conceptually necessary and is included in the nomologically necessary. Equivalently, on possibilities: nomological $\subset$ metaphysical $\subset$ logical.

Its standard sources. The claims usually offered as metaphysically necessary fall into a few families — identities between rigid designators (Hesperus is Phosphorus); constitution and origin (this table is made of this wood; Elizabeth came from these gametes); kind essences (gold has atomic number 79); mathematical and set-theoretic truths; and general principles about categories (no object is both abstract and concrete). What unifies them, on the dominant view, is that each holds in virtue of what the relevant things are.

Its analysis, and the dissent. The default framework is possible worlds: $\square p$ iff $p$ holds at every world, with S5 as the logic, so modal status is itself non-contingent. This is a semantics, not yet an explanation, and the explanatory question — what makes a world possible? — is where the positions divide:

• Lewisian modal realism takes worlds as concrete and primitive, so modality is analysed away into quantification over them, at the cost of a vast ontology.
• Ersatzism builds worlds from abstracta (maximal consistent sets of propositions, states of affairs), which keeps the ontology cheap but usually helps itself to a primitive modal notion ("consistent") in the construction.
• Essentialism (Fine, and the neo-Aristotelian revival) reverses the order of explanation: necessity is not the basic notion but is grounded in essence. Fine's counterexample is the lever — it is necessary that Socrates belongs to $\{\mathrm{Socrates}\}$, but nothing about what Socrates is concerns that set; so necessity is too coarse to capture essence, and essence must be prior. See Modality and Essence.
• Conventionalism and its heirs deny there is any worldly modality to explain: the necessities reflect our rules, and Kripke's a posteriori cases are handled by two-dimensional strategies on which what is discovered is empirical and what is necessary is analytic, split across two dimensions of content.

The deflationary family. The fourth option is the one the later sections of this remark keep returning to, so it is worth naming properly. To be a deflationist about metaphysical necessity is to hold that necessity is not a sui generis feature of reality that modal claims report, and to explain modal talk instead by something about us — our conventions, concepts, rules, or attitudes. The characteristic move is to accept the necessary truths while rejecting the realist's account of what makes them necessary. Three grades, in increasing order of concession to the realist:

Two clarifications keep the label honest. First, it is not deflationism about truth, discussed in the companion remark: that thesis rests on the redundancy of "is true," and there is no corresponding redundancy for $\square$ — necessarily $p$ plainly says more than $p$. The name travels; the structure does not. Second, and more importantly here, one can deflate the worlds without deflating the modality. Kripke's refusal to reify possible worlds, and modal fictionalism about them, are deflationary about the ontology of the semantics while remaining fully realist about modal facts. Throughout what follows, "deflation" means the reductive or expressivist thesis about necessity itself, not quietism about worlds.

What the deflationist owes, in return, is an account of two things: why modal claims feel like reports of how things must be rather than reminders of how we have agreed to speak, and how the a posteriori cases work — since a necessity that had to be discovered by experiment is the hardest thing for a conventionalist to accommodate, and was the reason Kripke's examples were taken to have finished the positivist programme off. The sections below ask whether those examples do as much damage as advertised.

Its epistemology — the standing problem. If metaphysical necessity is neither analytic nor empirical, how is it known? The usual answer is conceivability as a guide to possibility, which Kripke's own cases immediately embarrass: one can seemingly conceive water not being ${\mathrm{H}}_2\mathrm{O}$, yet it is impossible. The standard repair distinguishes what is genuinely conceivable from what merely seems so because an epistemic counterpart (a watery stuff that is not ${\mathrm{H}}_2\mathrm{O}$) is being conceived instead. Whether this repair is principled or ad hoc — and whether modal intuition tracks anything at all — remains the sharpest objection to the whole enterprise, and it is the pressure point for zombie arguments in philosophy of mind and for modal ontological arguments in philosophy of religion.

Where Kripke himself stands

Since the case for metaphysical necessity is largely his, it is worth asking which of the positions above he occupies. The short answer is realist, but minimally so — and none of the four analyses is his. Kripke reopened the subject without building a theory of it, and the gap between what his arguments establish and what he was willing to assert is easy to miss.

• Realist about modal facts. Necessity for Kripke is a metaphysical notion, contrasted explicitly with the epistemic (a priori) and the semantic (analytic). De re modal predication is intelligible, essentialist claims are true, and their truth is not about our concepts or conventions. Against Quine, this is a substantive realism: the world settles the modal facts.
• Primitivist, not reductionist. He offers no analysis of necessity in terms of anything more basic. Where Lewis reduces modality to quantification over concrete worlds, Kripke leaves $\square$ unanalysed and elucidates it by cases. He supplied the formal semantics for modal logic, but that is a mathematical tool, not a metaphysics — the model theory does not tell you what makes a world possible.
• Deflationary about possible worlds. This is where "realist" most misleads. A possible world for Kripke is a counterfactual situation, a way things might have been — not a place, and emphatically not something discovered by looking. He warns that the "worlds" metaphor has done damage, prefers talk of possible states or histories of the world, and holds that worlds are stipulated: we specify a situation as one concerning this very object. Hence his rejection of Lewis's counterpart theory — if what matters to Humphrey's having won is a similar man's winning somewhere else, the theory has changed the subject. So he is an anti-reductive actualist, not a modal realist in Lewis's sense.
• Modal, not Finean, about essence. Kripke reads an essential property as one a thing could not have lacked — the modal conception of essence. He does not ground necessity in essence; the explanatory order runs the other way. This is precisely the account Fine later attacked with the Socrates/singleton case, so Kripke is on the opposite side of that dispute from the neo-Aristotelians who cite him.
• Intuition as evidence. His methodology is candid: intuitive content counts as very strong evidence, and he doubts anything more conclusive is available. This is a realist epistemology of modality with no theory attached, and it is the flank the conceivability critics attack.
• The a priori conditional is his own. The structure isolated in the sections below — empirical premise plus an a priori essentialist principle — is not a hostile reconstruction. Kripke states it himself: one knows a priori that if the table is made of that wood it is necessarily so made, and empirical work supplies the antecedent. What he denies is the further Sidelle-style claim that the a priori principle is conventional; for Kripke it is a substantive a priori metaphysical truth.

The upshot is a position often labelled non-reductive modal realism or modal primitivism: objective modal facts, no analysis of them, and studied quiet about the ontology of worlds. Its strength is that it does not have to defend Lewis's plenitude or ersatzism's circularity. Its cost is that the explanatory questions — what makes a possibility possible, why these properties are essential, how intuition tracks any of it — are left open by design, which is why the deflationary pressure explored below has somewhere to push.

The ambiguity in "water is H₂O"

The example carries more weight than any other in the modal literature: it is the standard illustration of the necessary a posteriori, the standard evidence for kind essences, and the standard fixed point against which theories of conceivability are calibrated. It is also not a single claim. "Water is ${\mathrm{H}}_2\mathrm{O}$" is ambiguous in both flanks and the copula, and the readings differ precisely in their modal status. The suspicion worth pressing is that the example looks compelling because it borrows its necessity from one reading and its empirical content from another.

Disambiguating. At least four claims hide under the sentence:

The pressure is the first row against the second. "A water molecule is an ${\mathrm{H}}_2\mathrm{O}$ molecule" is precise and unimpeachable, but it is necessary in the cheap way: at the molecular level "water molecule" and "${\mathrm{H}}_2\mathrm{O}$ molecule" are two notations for one thing, and no world could contain a water molecule that was not one, for the same reason no world contains an unmarried bachelor. Nothing metaphysical has been established. The substantive claim is about the stuff — the liquid in lakes, the thing baptised — and that is the reading on which the chemistry was a discovery.

But the stuff reading is not literally true. Liquid water is not a heap of isolated ${\mathrm{H}}_2\mathrm{O}$ units. It is a fluctuating hydrogen-bonded network with continual proton exchange, so a real sample always contains ${\mathrm{H}}_3{\mathrm{O}}^{+}$, $\mathrm{O}{\mathrm{H}}^{-}$, and transient oligomers alongside monomers; natural samples also mix isotopologues ($\mathrm{HDO}$, ${\mathrm{D}}_2\mathrm{O}$, ${\mathrm{H}}_2^{18}\mathrm{O}$). Read as a strict claim about what a sample consists of, "water is ${\mathrm{H}}_2\mathrm{O}$" is false; read as a claim about stoichiometric composition under idealisation, it is true but is no longer an identity of kinds — it is a statement about a ratio that holds of an idealised pure sample. (The chemical details are set out in Natural Kinds.)

And "is" is doing three jobs. Identity ("the kind water = the kind ${\mathrm{H}}_2\mathrm{O}$"), predication of composition ("water has formula ${\mathrm{H}}_2\mathrm{O}$"), and constitution ("water is made of ${\mathrm{H}}_2\mathrm{O}$"). Only the first feeds the argument, because the route to necessity runs through the necessity of identity: $a=b\to \square (a=b)$, given rigidity. Constitution will not do the same work — as the material constitution debate makes plain, x can be constituted by y without being identical to it, and the relation is standardly contingent.

What the necessity therefore assumes. Once disambiguated, the modal claim is seen to rest on several premises that chemistry does not supply:

1. That there is a kind identity to be had at all — that the macroscopic substance and the molecular species are one kind rather than two levels related by constitution.
2. Microstructural essentialism. That the essence of a stuff is compositional rather than macroscopic. Nothing empirical decides this: Needham's alternative individuates water thermodynamically, by its phase diagram and behaviour as a substance, and the choice between the levels is a metaphysical decision made before the chemistry is consulted.
3. A determinate same-substance relation. Putnam's schema — x is water iff x bears the same-liquid relation to the baptismal sample — needs that relation to be sharp. It is not. Same what? Same stoichiometry admits ${\mathrm{D}}_2\mathrm{O}$; same isotopic constitution excludes ordinary tap water, which is a mixture; same phase behaviour excludes ice and steam, which the kind reading must include. The qua-problem: ostending a sample does not fix the level at which sameness is to be judged, so it does not fix the kind.
4. Rigidity on the right-hand flank. The necessity of identity requires both terms to be rigid designators. "${\mathrm{H}}_2\mathrm{O}$" is a compositional formula; if it functions as a description — the stuff whose molecules have that composition — then Kripke's own modal argument against descriptivism applies to it, and the flank is not rigid. The reply, that chemical formulae are rigid because composition is essential, simply reasserts assumption 2.
5. An a priori conditional. This is Kripke's own reconstruction, and it is the decisive one. The empirical work establishes only the actual fact. Getting to $\square$ requires the further principle that composition is essential to a substance — i.e. the a priori conditional if water is ${\mathrm{H}}_2\mathrm{O}$, then necessarily water is ${\mathrm{H}}_2\mathrm{O}$. Chemistry discharges the antecedent; the essentialist premise supplies the box.

A circularity in the supporting thought experiment. Twin Earth is usually offered as evidence for kind essentialism: XYZ is superficially indistinguishable from water yet is not water, so microstructure fixes kind membership. But the verdict that XYZ "is not water" is only compelling if one already holds that microstructure fixes kind membership. A Needham-style opponent, individuating by macroscopic behaviour, will say Twin Earthians have water and we were wrong about its composition. The thought experiment elicits the assumption; it cannot confirm it.

What survives. Not much is lost for the necessary a posteriori in general. Hesperus is Phosphorus is untouched by this particular objection — a genuine identity between one object and itself, with two rigid names, no level ambiguity and no constitution/identity slippage (a separate caveat about that case is entered below). What is impugned is the use of "water is ${\mathrm{H}}_2\mathrm{O}$" as a free-standing illustration of worldly necessity, since it smuggles in an unstated essentialist premise and trades on the drift between the molecular and substance readings. The defensible residue is conditional: given that kinds have microstructural essences and that composition is the relevant one, water is necessarily ${\mathrm{H}}_2\mathrm{O}$ — with the empirical discovery and the necessity attaching to different components of the claim.

The general lesson. Every cross-level identity of this form — heat is molecular motion, gold is the element with atomic number 79, genes are DNA sequences, pain is C-fibre firing — requires the level of description to be fixed before its modal status can even be assessed, and fixing the level is metaphysics, not science. Gold is $Z=79$ is the healthiest case, because chemical practice really does define element identity by proton count, so the level is settled by the discipline itself; the mental-state cases are the worst, which is why the zombie literature spends most of its energy exactly here. But the health of the gold case is bought at a price, and the next section is about the bill.

"Gold is the element with atomic number 79": discovery or definition?

The gold case is usually offered as the clean one — where water strains against the chemistry, gold has a single stable isotope, an unambiguous proton count, and a criterion the discipline itself endorses. That cleanliness invites a deflationary suspicion. If modern chemistry defines an element as a species of atoms sharing a proton number, then "gold" and "the element with atomic number 79" are two labels the framework assigns to one cell of the periodic table, and their necessary co-application looks like a fact about the labelling scheme rather than a discovery about the world. On this reading the modal force of the claim is borrowed from a stipulation of nomenclature: within the system the two expressions are made to co-refer, so of course nothing counts as one without counting as the other.

First, a repair to the inference. Co-reference by itself never yields necessity. "The number of planets" and "$8$" refer to the same thing, yet the number of planets is $8$ is contingent — the planets might have been fewer. What converts co-reference into necessity is rigidity on both flanks plus the necessity of identity, so the argument needs the extra premise that the element with atomic number 79 designates rigidly rather than picking out whatever occupies that slot at a world. That premise is available — but noting that it is needed already shows the necessity is not delivered by sameness of reference alone.

Second, the deflationary observation is largely correct about the chemistry. Elements were not always individuated by proton number. Through the nineteenth century they were individuated by atomic weight and chemical behaviour; the discovery of isotopes broke that criterion, since chemically inseparable samples turned out to have different weights, and Moseley's 1913 X-ray work supplied the replacement by showing that nuclear charge, not weight, gives the periodic ordering. The modern definition — an element is a species of atoms with a given number of protons — is the result of that revision. So two distinguishable things happened: an empirical discovery (the samples we had been calling gold are composed of atoms with 79 protons) and a decision (that proton number, rather than weight or chemical profile, is what makes something the element it is). The identity statement is a discovery only on the first count; on the second it records a criterion adopted, and once adopted, "gold is the element with atomic number 79" is analytic within the framework.

Third, the Kripkean reply, which is not to be brushed aside. The necessity claimed is de re, not metalinguistic. It is entirely contingent that the word "gold" refers to what it does — English might have used it for platinum — and Kripke never denies this. What he claims is that that very kind, however named, could not have had a different nuclear charge. Sliding between the metalinguistic contingency and the de re necessity is exactly the confusion his framework was built to prevent, and a deflation phrased as "the two phrases were given the same reference" is at risk of it: the sentence is about gold, not about "gold." The framework fixes which claim is expressed; it does not thereby make the claim be about the framework.

Fourth, the conventionalist's best version survives that reply. The sophisticated deflation (Sidelle; and behind it Carnap's framework-internal analyticity) grants that the de re claim is well-formed and concedes the empirical part outright, then locates the modal component elsewhere. The argument runs: an a priori, framework-supplied principle — if a substance is individuated by nuclear charge, it has its nuclear charge essentially — plus an empirical premise about which charge the samples have. Chemistry discharges the empirical premise; the necessity comes from the principle, which is a convention about how we individuate substances. This is the same structural point as the fifth assumption in the water case above, and it is why the two examples belong together: in both, the a posteriori and the necessary attach to different premises, and only the a posteriori one is answerable to the world. Two-dimensional semantics is the same manoeuvre in a formal key, with the analytic component along the primary intension and the necessity along the secondary.

Fifth, why the convention is nonetheless not arbitrary. The realist's strongest move is not to deny that a criterion was chosen but to argue the choice was forced by explanatory depth. Proton number fixes nuclear charge, which fixes electron configuration, which fixes chemical behaviour — the whole periodic system is derivable in that direction and in no other. Gold's colour is a case in point: it is yellow rather than silvery because relativistic contraction of the $6s$ orbital narrows the $5d\to 6s$ gap into the visible range, an effect that is a consequence of $Z=79$. So the framework's criterion is not a label pinned on arbitrarily; it names the property from which the rest of the kind's profile follows. But this vindicates the choice as well-motivated, which is a weaker status than necessary — a criterion can be uniquely explanatory without its adoption being a modal discovery.

Where the seams show. The convention is doing visible work at the margins, which is the evidence that it is a convention:

• Ions and plasmas. $\mathrm{A}{\mathrm{u}}^{3+}$ has 79 protons and almost none of gold's chemical or physical profile. If elementhood is proton number, it is gold; if it is chemical behaviour, it is not. Chemistry answers "gold" — because it chose the nuclear criterion.
• Isotopes. Gold's cleanliness here is luck: ${}^{197}\mathrm{Au}$ is its only stable isotope, so the isotope problem that afflicts water never arises. Take an element with several and the same questions return.
• Superheavy elements. Relativistic effects make the heaviest elements behave unlike their periodic-table groups, so chemical behaviour and proton number can come apart. That chemists follow proton number anyway, and re-describe the anomalous chemistry, shows which criterion is treated as constitutive — a methodological commitment, not a finding.

Sorting the claims. The suspicion is right about some of what is asserted and not about all of it:

The deflation succeeds against a conflation of the fourth row with the first and third, and that conflation is common in casual presentations of the example. It does not by itself refute the fourth row, because the de re claim is not about words. What it does establish is the more modest and more interesting result: the sciences supply criteria of individuation, and reading a criterion as an essence is a further step taken by the metaphysician. Chemistry says: for our purposes, count atoms as the same element when their nuclear charges agree. Whether that classificatory decision reports what gold is, in a sense that constrains every possible world, is exactly the question the science was not asking — and it is the same question left open by ontology under theory change and by the Carnapian treatment of framework-internal truth.

Does the de re claim presuppose a theory of reference?

The last two sections both leaned on the same defence: the necessity is de re, about the stuff rather than the word, so a deflation about labelling misses its target. That defence deserves the pressure it invites. The fourth row above was stated with a proper name and a definite description; its de re reading is secured by a scope decision about where the description sits relative to $\square$; and its determinacy across worlds is underwritten by rigidity. Name, scope, rigidity — every part of the apparatus that makes the claim available is machinery from the philosophy of language. So the reply "it is not about words" is itself issued from inside a theory of how words work.

Two senses of "presuppose," and only one is damaging. The distinction to hold onto is between what a claim needs in order to be expressed and defended and what its truth consists in.

• Expressive dependence. To state that gold is necessarily $Z=79$, one must refer to gold, and referring is a linguistic act governed by whatever the correct semantics turns out to be. This is undeniable and also proves far too much: the cat is on the mat presupposes a theory of reference in exactly the same way. Every assertion whatever is expressed in language; if that sufficed to make a claim's subject-matter linguistic, there would be no non-linguistic subject-matter at all.
• Constitutive dependence. The stronger charge is that the claim's truth-conditions involve facts about language — that what makes it true is something about how English and chemical nomenclature are set up. This is what the deflationist needs and what the Kripkean denies: the truth-conditions involve gold, nuclear charge, and possible worlds, none of which are words.

So the bare observation that a theory of reference is in play does not settle anything. The reply survives at the level of content while conceding the level of expression.

But the concession is less harmless than it sounds. Three points keep the worry alive rather than dissolving it.

1. The rehabilitation of de re modality was itself a semantic achievement. Quine's objection — that necessity attaches to objects only relative to how they are described, so quantifying into modal contexts is unintelligible — was not answered by metaphysics. It was answered by showing that names are rigid, hence that substitution into modal contexts is legitimate. The intelligibility of the fourth row is therefore downstream of a thesis about reference. One cannot both take the benefit of that thesis and claim independence from it.
2. Trans-world individuation is stipulated, not found. Kripke's own answer to "how do we identify gold in another world?" is that worlds are stipulated, not inspected — we specify the counterfactual situation as one concerning this kind. That is a decision about how our terms are to be used in describing possibilities. Counterpart theory makes the dependence explicit and unavoidable: with no trans-world identity, de re modal predication is relative to a counterpart relation, and which relation is operative shifts with how the object is described — Lewis's inconstancy of de re modality. Whether de re claims have description-independent truth-values is thus not a datum but a consequence of a contested package.
3. The qua-problem, and the evidence base. Ostending a sample does not by itself fix which kind was baptised — this stuff qua element? qua metal? qua yellow substance? — so the causal chain needs a descriptive supplement to determine the subject of the de re claim, reintroducing exactly what rigidity was meant to displace. And the working evidence for essentialist verdicts is intuitions about what we would say of described cases. Intuitions elicited by sentences are an uncomfortable evidence base for a thesis whose whole point is that the necessity is not about sentences.

The symmetry, which is the decisive point. None of this hands the argument to the deflationist, because "the necessity is just two expressions assigned the same reference in a system" is also a claim made from inside a theory of language — a broadly descriptivist or conventionalist one, on which meaning-assignments fix modal profiles. It is not the neutral, theory-free observation it presents itself as; it is the denial of rigidity, which is a substantive semantic thesis with its own well-known costs (the modal, epistemic, and semantic arguments above). Neither party occupies language-neutral ground. The real shape of the dispute is therefore not worldly necessity versus linguistic necessity, but a choice between two packages, each pairing a semantics with a metaphysics — and the choice is made on the usual grounds of overall cost and fit, not by one side catching the other out in a use/mention slip.

The attempt to step outside. The neo-Aristotelian program is best read as an effort to state the metaphysics without borrowing the semantics. Fine's real definition takes essence as primitive and non-modal — what it is to be gold, in the way Aristotle distinguished definitions of things from definitions of names — with necessity derived from essence rather than analysed as truth in all worlds. If that idiom is coherent, the essentialist claim can be made without routing through rigidity or trans-world identification, and the present objection lapses. The open question is whether "real definition" is intelligible independently of the linguistic notion it is named after, or whether it merely relocates the appeal to how we specify what a thing is. See Modality and Essence.

The honest scoreboard. The de re claim does not presuppose a theory of reference for its truth, and the deflation fails if it is meant to show otherwise. But the claim is only available, only intelligible, and only assessable within some such theory — and the theory that makes it look obvious is contested. What that leaves is not a refutation of metaphysical necessity but a recalibration of how much the standard examples prove: they are not neutral data points that force essentialism on anyone, but consequences of a semantic framework that has to be argued for on independent grounds.

Is even Hesperus is Phosphorus framework-relative?

Twice above, the Venus case was held back as the clean one — a genuine identity of an object with itself, immune to the level-ambiguity that afflicts water and the criterion-dependence that afflicts gold. It is worth asking whether it is really so well insulated, and the natural way to press is by contrasting in every possible world, the morning star is the evening star with in astronomy as we know it, the morning star is the evening star.

The first correction is internal to Kripke. Stated with those phrases as definite descriptions — the brightest object in the eastern sky before dawn, the brightest in the western sky after dusk — the identity is contingent, and Kripke says so himself. Descriptions are not rigid: in a world where Mars is the brightest morning apparition and Venus the brightest evening one, the morning star is not the evening star. Necessity requires reading "Hesperus" and "Phosphorus" as names that those descriptions were used to introduce — reference-fixing without synonymy. So the canonical example carries a third ambiguity, structurally parallel to the two already seen: not a level ambiguity as with water, nor a criterion ambiguity as with gold, but a rigidity ambiguity between the name and description readings, with opposite modal verdicts on either side.

And the necessary residue is thin. Once both flanks are read as rigid names, what is necessary is that Venus is Venus. The necessity of identity then follows as a near-theorem: from $x=y$ and $\square (x=x)$, Leibniz's Law delivers $\square (x=y)$. No essentialist premise is required anywhere. But the same feature that makes the necessity secure makes it uninformative — the substantive astronomical discovery is that the morning apparition and the evening apparition belong to one body, and that claim, being about apparitions picked out descriptively, is contingent. The necessity and the informativeness once again attach to different components, which is Frege's puzzle stated modally.

Now the framework question. Distinguish three grades of framework-dependence, only the last of which is peculiar to modality:

This is where the Venus case genuinely does better than the other two. At grade 3 it is untouched: gold and water need the essentialist bridge — composition is essential, nuclear charge is essential — and that bridge is framework-supplied, whereas the identity of an object with itself needs nothing but rigidity and Leibniz's Law. The astronomy contributes the a posteriori premise and no part of the modal one.

But grades 1 and 2 still bite, and grade 2 bites harder than it looks. To assert the identity at all is to treat Venus as a persisting body whose morning and evening apparitions are stages or appearances of one thing. That presupposes an ontology of enduring individuals with trans-temporal identity conditions — a framework commitment, and a contested one, as the persistence and material constitution debates show. It presupposes that identity is determinate, which is precisely what fails for quantum indistinguishables, where whether one has one particle or two may have no fact of the matter. And it presupposes classical logic with unrestricted substitution into modal contexts. Strip the framework of persisting bodies and the sentence does not become false; it becomes unstatable.

The realist's rejoinder, which is strong. "In astronomy as we know it" is an epistemic qualifier — it marks how we came to know and flags our fallibility. We might yet be wrong that there is one body; but from "we can establish $p$ only within framework $F$" it does not follow that "$p$ is true only relative to $F$." That inference is the modal fallacy the whole subject is built to avoid, and it is the same conditional structure as before: the framework discharges the antecedent, and if Hesperus is Phosphorus, then necessarily it is. There is also a striking piece of evidence on the realist's side here that is absent in the other two cases: the identification is robust across radical theory change. Babylonian astronomers already tracked Venus as a single body through its apparition cycle, the identification is credited in Greek antiquity to Pythagoras or Parmenides, and it survived intact through Ptolemaic, Copernican, Newtonian, and relativistic astronomy — while almost every surrounding concept (sphere, planet, mass, orbit) was rebuilt. A claim that persists across that much theory change is poor evidence for framework-constitution.

Where this leaves the question. Metaphysical necessity does presuppose a framework at grades 1 and 2 — always, and unavoidably, since a claim must be expressed and its subject individuated before it can be evaluated. It presupposes one at grade 3 only for the kind-essentialist necessities, which is exactly why water and gold are vulnerable in a way Venus is not. But there is an uncomfortable consequence for the essentialist even so: strip out the framework's contributions from all three of the standard examples and the surviving necessity is $a=a$. Water's necessity needed an essentialist premise; gold's needed a criterion the discipline chose; Venus's needs neither, but delivers only self-identity dressed in two names. That the residue is a logical truth is precisely the conventionalist's thesis — all necessity is analytic at bottom — reached this time by working through the realist's own best cases rather than by denying them.

The realist need not concede, and the honest terminus is that the dispute has stopped being about modality. Whether individuation at grade 2 is discovered or constituted is the general realism question about science and reference, and the answer one gives there determines the answer about necessity rather than the other way round. Modal metaphysics inherits that problem; it does not have a special one of its own.

Can the discovery be explained away as the making of a convention?

The deflationary strategies so far have been analytic: separate the readings, isolate the premises, ask which flank is rigid. There is a historical version that is more direct, and it targets the one component the conventionalist has always found hardest — the a posteriori part. The proposal is that if one traces how the identification was actually made, standardised, and entrenched by a scientific community, the whole appearance of discovering a necessity dissolves into the ordinary business of adopting a convention and then living inside it. There is no modal fact to be found at the end of the story, because the story is about the formation of a criterion.

How a criterion hardens. The mechanism is well documented and looks the same across cases:

1. Correlation. An empirical regularity is established — samples of this stuff decompose into these gases in this ratio; these atoms show this X-ray spectrum.
2. Promotion. The correlation is adopted as the test for membership, because it is explanatorily deeper and practically more robust than the superficial marks it replaces.
3. Entrenchment. The test is written into nomenclature, textbooks, standards bodies, and instrument calibration. It stops being something one checks and becomes something by which other things are checked.
4. Modalisation. Since nothing now counts as the kind without satisfying the test, no describable case comes out as a counterexample — and that unfalsifiability-in-practice is read back as a discovery that the world could not have been otherwise.

Step 4 is where the alleged illusion is manufactured. On this account "necessarily, water is ${\mathrm{H}}_2\mathrm{O}$" reports the terminal state of a social process, and the sense of having found something out belongs to step 1, which established only a contingent correlation.

The historical record supplies the evidence. What makes the story more than speculation is the supply of claims that once functioned exactly as necessities and were later given up. Euclidean geometry was the paradigm of synthetic a priori necessity until general relativity; absolute simultaneity was not a hypothesis anyone tested; elements were individuated by atomic weight until isotopes forced the change; atoms were indivisible by definition; whales were fish. In each case the claim was not refuted the way an ordinary hypothesis is refuted — the framework was rebuilt around it. This is Reichenbach's and Friedman's relativized a priori: principles that are constitutive within a framework, genuinely a priori relative to it, and revisable when it is replaced. It is Putnam's point in It Ain't Necessarily So, Quine's picture of statements near the centre of the web insulated from revision by their position rather than by their subject matter, and Poincaré's conventionalism about geometry and the hardening of empirical laws into disguised definitions. Chang's history of the chemical revolution makes the same case on the very example at issue.

Two arguments here, and only one is any good. They are easily run together and have very different strength.

• The genetic argument — the claim was arrived at by a contingent social process, therefore it is not a necessary truth about the world. This is fallacious as it stands. How a belief was acquired settles nothing about its content or its modal status; the metre's history is a tangle of committee decisions, and facts about lengths are not thereby conventional. Every discovery whatever has a messy institutional history.
• The explanatory-redundancy argument — everything the claim does (licensing inferences, excluding cases, functioning as a criterion, resisting revision) is fully accounted for by the norm that was installed, so the postulated modal fact does no work. This is a real argument, of the same form as any appeal to ontological parsimony, and the history functions as evidence for it rather than as the argument itself.

Keeping these apart matters, because the realist's stock reply refutes only the first.

The realist's reply, and its cost. Fallibility about necessity is not the absence of necessity. Euclidean geometry was never necessary; we were wrong to think it was — and the Kripkean structure predicts exactly this, since the a priori conditional yields $\square P$ only given a true antecedent, and antecedents can be got wrong. Every item on the historical list is then rediagnosed as an error about which claims are necessary, leaving the category intact. This is coherent and, on the merits, probably right. But it should be noticed what it costs: no possible history of revision could ever count against the position, since each revision is absorbed as a correction to the antecedent. A thesis insulated from the entire empirical record in that way is not thereby false, but it can no longer cite the record as support either — and it is the same insulation that makes the appeal to modal intuition uncomfortable.

Why the history cannot decide it. The deeper problem for the proposal is that both hypotheses predict the same historical process. A community genuinely tracking a real essence would also proceed by correlation, promotion, entrenchment, and eventual treatment of the criterion as non-negotiable — that is simply what the discovery of deep structure looks like from inside an institution. The four-stage story is therefore compatible with realism, and produces the deflationary conclusion only if one has already decided that nothing lies behind step 2. What the genetic analysis genuinely achieves is narrower and still worth having: it removes the argument from obviousness. Once one sees how the criterion was installed, the sense that its necessity is simply evident is no longer available as evidence, and the realist has to argue rather than point.

The discriminating test. What separates the two hypotheses is not the existence of a process but the presence of live alternatives within it. If the record shows that a rival criterion was available and workable, and that the winner was chosen for tractability, convenience, or institutional momentum, the deflationary reading is supported. If the criterion was effectively forced — nothing else could have organised the phenomena — then the process looks like discovery under institutional conditions. Applying that test ranks this remark's three examples, and the ranking is the same one the earlier sections reached by other routes:

So the answer to the proposal is a qualified no with a substantial concession. The empirical component cannot be explained away, because the correlations at step 1 were genuinely found and not stipulated, and because the process is neutral between the competing accounts of what was going on. But the modal component can very often be traced to steps 2 and 3 — and where the record shows a criterion selected from live alternatives, the burden shifts to the realist to say why that selection tracked an essence rather than constituting one.

Is the dispute merely notational? Translation between the idioms

Every section above has ended in the same shape: the two parties agree on all the chemistry, all the astronomy, and all the first-order modal verdicts, and disagree only about what the necessity consists in. That pattern is the signature of a dispute that might be merely verbal — and the way to test it is to ask whether a systematic translation between the idioms exists. If "rigid designator" can be replaced throughout by "term whose reference the framework holds fixed," and every realist sentence thereby mapped to a deflationist one and back, then the appearance of disagreement may be an artefact of two notations for one theory.

The dictionary one would need. The proposed mapping is not hard to write down, at least schematically:

There is a precedent, and it is cautionary. This is not a new manoeuvre: Lewis gave an explicit, purely syntactic translation scheme from quantified modal logic into the language of counterpart theory, with mechanical rules for eliminating $\square$ and $◊$ in favour of quantification over worlds and counterparts. It was rejected — and rejected on two grounds that both recur here. Kripke's objection was that the translation changes the subject: what matters to Humphrey is his own winning, not a similar man's. And formally, the translation fails to preserve theorems the realist takes as central, since counterpart relations need not be one-one and the necessity of identity can come out false. A translation can exist, be perfectly systematic, and still be rejected as inadequate to what it translates.

The best actual candidate already exists. The proposed replacement of rigidity by framework-relative reference is more nearly realised than it might appear: two-dimensional semantics is precisely a framework in which rigid designation and framework-relative reference are two coordinates of one formalism. The primary intension maps a context, considered as actual, to a referent — that is "reference inside a framework," the descriptive, a priori accessible dimension. The secondary intension holds the referent fixed and varies the world of evaluation — that is rigidity. Kripke's cases are then modelled without dispute by either side: water is ${\mathrm{H}}_2\mathrm{O}$ has a contingent primary and a necessary secondary intension, which is exactly why it is a posteriori and necessary at once.

And here is the instructive part: both camps accept the formalism, and the disagreement survives it intact. What they disagree about is which dimension reports reality — whether the secondary intension tracks a worldly essence, or merely records the convention that reference be held fixed once the primary intension has done the referring. The translation is available; it does not dissolve anything. It relocates the dispute from the object language to the question of which coordinate of a shared formalism is metaphysically privileged, which is not a question the formalism can answer.

What equivalence would even be required. Sharpening "syntactic translation" helps see why success would prove less than hoped. Mere mutual interpretability — each theory interpretable in the other — is far too weak, since interpretability is routine between theories no one regards as saying the same thing. What would be needed is something like definitional equivalence: each side able to define the other's primitives and recover its theorems. But even that is an equivalence of syntax and ontology, not of what Quine called ideology — the notions taken as primitive. Two definitionally equivalent theories can differ over which notions are basic, and that is precisely what realist and deflationist disagree about: whether $\square$ or the framework rule is the primitive. Formal equivalence leaves explanatory priority untouched.

Three places the translation leaks. Beyond that general point, the mapping breaks down at identifiable joints:

1. Indexation destroys absoluteness. The realist's $\square$ is unrelativised; the deflationist's rendering is ${\square }_F$. Nothing in the deflationist's language translates the realist's claim that a proposition is necessary simpliciter, and the difference shows up in the logic: since $F$ itself could have been otherwise, "$p$ is constitutive of $F$" is not itself constitutive of $F$, so the natural rendering does not validate $\square p\to \square \square p$ and the S5 structure the realist assumes is lost. The deflationist can either accept a weaker modal logic or index the indexing, which regresses.
2. Error becomes mere change. The realist can say that our framework gets the essences wrong — that we may be mistaken about what is necessary. Translated, this becomes only "$F$ may be replaced by $F^{\prime }$ in which $p$ is not constitutive," which records a difference, not a mistake. The distinction between correction and revision has no deflationary image, and it is the standard place where relativising theses lose something they need.
3. Agreement on assertions is not agreement on grounds. Even where the mapping runs smoothly, the two theories give incompatible answers to why the sentences hold. Empirical equivalence has never been sufficient for theoretical identity, and there is no reason for modality to be the exception.

The parallel with quantifier variance is exact. This is the same argument that runs in meta-ontology: Hirsch's quantifier variance holds that disputants in ontology can each interpret the other charitably so that both speak truly, making the dispute verbal. Sider's reply is that intertranslatability does not entail parity — one language may carve at the joints better than another, and which does is a further, non-verbal question about structure. Transposed here: even a perfect manual between the modal idioms would leave open whether necessity or convention is the more natural primitive, and the realist's claim was always the naturalness claim, not a claim about which sentences to assert. Whether that residual question is substantive or itself a pseudo-question is the ontological realism debate in miniature, which is where this remark's arguments have repeatedly terminated.

Verdict. A translation is largely constructible for first-order modal claims, and two-dimensionalism supplies most of it already. It is not constructible at the metalevel, where the realist's absolute $\square$, the notion of modal error, and the explanatory ordering of $\square$ against framework rules all fail to survive the mapping. So the dispute is not merely verbal — but it is narrower than it looks: not a disagreement about what is necessary, but about which of two intertranslatable vocabularies is the fundamental one. That is exactly the pattern every earlier section ran into, and it explains why the chemistry, the astronomy, and the history could never settle the question. They are on the translatable side of the line.

The balance sheet: what each side leaves unexplained

If the choice between the vocabularies is settled on overall cost and fit rather than by decisive argument, the costs had better be stated explicitly. They are unusually well matched, and they pair off: each side's principal debt is the other's principal asset.

The realist's three real debts. The first is the access problem, and it is the serious one: it is the modal analogue of Benacerraf's objection to platonism about mathematical objects, and it has the same shape — a domain of mind-independent facts with which we have no causal commerce, plus a faculty (intuition) whose reliability about them is asserted rather than explained, and for which no evolutionary or mechanistic story is on offer. The second is the absence of a criterion: origin and constitution are essential, colour and location are not, and nothing in the theory predicts this — the verdicts are collected, not derived. The third is persistent disagreement: competent, fully informed philosophers do not converge on the modal cases the way chemists converge on chemistry, which is awkward for the claim that a shared subject-matter is being perceived. To these should be added the insulation noted earlier — every historical revision is absorbed as an error about an antecedent, so the record can neither confirm nor disconfirm.

The deflationist's three real debts. The first is that nobody can state the convention. The account requires an analytic individuating principle — substances are individuated by composition — that appears in no dictionary, is taught to no one, and is consciously held by nobody, yet is supposed to be doing all the modal work. Worse, the position needs analyticity as a going notion, and Quine's demolition of it damages the conventionalist at least as much as the realist. The second is non-optionality: conventions are ours to revise, yet we cannot decide that water might not have been ${\mathrm{H}}_2\mathrm{O}$ — and the reply that we would then be talking about something else concedes that something outside the convention constrains what happens when we try to change it. The third is that the expressivist branch inherits the Frege–Geach problem: modal claims embed in conditionals, disjunctions, and attitude reports, and a theory on which asserting a necessity conveys a rule rather than describes a fact owes an account of what the embedded occurrences are doing.

The pressure point they share. Both accounts converge on the same sentence and both find something uncomfortable there. The a priori conditional — if water is ${\mathrm{H}}_2\mathrm{O}$, then necessarily it is — is, for the realist, a substantive truth about the world known a priori, which is precisely the category post-Quinean epistemology denies exists. For the deflationist it is analytic, which requires the notion of analyticity that the same critique destroyed. The disagreement is about the status of one premise that neither side can comfortably account for, which is a good indication that the difficulty is not the property of either position.

The trade in one line. The realist buys objectivity, error, and the phenomenology of discovery at the price of epistemology and criterion; the deflationist buys epistemology and criterion at the price of objectivity, error, and the reliability of modal reasoning. This is not a coincidence of this debate: it is the generic shape of realism disputes, the same trade struck in the philosophy of mathematics between access and objectivity, and in metaethics between explaining moral knowledge and explaining moral error. Recognising the shape is useful mainly as a warning that the local arguments are unlikely to settle anything the global ones have not.

Where the hybrids try to pay. Each middle position is an attempt to buy one asset without the corresponding cost, and it is worth being clear about which debt each targets:

• Williamson's counterfactual account attacks the realist's access problem head-on: modal knowledge is a by-product of the ordinary capacity to evaluate counterfactuals, which is independently indispensable and uncontroversially reliable, so no special faculty is required. It leaves the criterion problem untouched.
• Fine's essence-first realism attacks the criterion problem: real definition supplies a principled source for the necessities instead of a list. It makes the epistemology harder, not easier.
• Thomasson's normativism claims both columns at once — the rules plus the empirical facts jointly determine determinate answers, so objectivity is recovered without worldly modality. Whether that is a solution or a relabelling is the live question about it.
• Two-dimensionalism declines to choose, keeping an a priori dimension and a necessary dimension and assigning the debts to different coordinates — which, as the previous section noted, postpones the question rather than answering it.

There is no free lunch on offer. What would count as progress is not a new argument about water or gold — those have been exhausted above — but an account of modal epistemology good enough to discharge the realist's first debt, or an articulation of the alleged conventions explicit enough to discharge the deflationist's. Both remain open, which is the honest reason the dispute persists.

Related: Possibility and Necessity (the flavours of modality, de re / de dicto, the modal logics), Possible Worlds (what worlds are), Essence and Accident, Natural Kinds (how far chemistry and biology cooperate with kind essentialism), Material Constitution, Identity (the necessity of identity), Meta-Ontology: Carnap and Quine (framework-internal truth), and Semantics and the Theory of Meaning (reference, rigidity, externalism).