David Lewis began with counterpart theory in the 1960s, added the analysis of counterfactuals in the early 1970s, and over the following decades built the most extravagant ontology any analytic philosopher has ever defended. When you say “I could have taken the other job,” Lewis holds, you are saying truly that somewhere, in a universe spatiotemporally isolated from this one, a person who resembles you in the relevant respects took that job. The universe is concrete: just as concrete as this one. It contains stars and tables and chairs. You will never causally interact with it. But it exists, full stop, in exactly the sense this one does. Modal language is not abstract after all. It is a report on a plurality, and the plurality is the ontology.

Lewis developed Modal Realism across two decades, in *Counterfactuals* (1973) and *On the Plurality of Worlds* (1986), one of the most systematic books of late analytic metaphysics. The position remains his alone: its orbit has structured a generation of work on modality without persuading others to adopt the concrete plurality unchanged. Divers (2002) and Nolan (2002) develop Lewisian variants with modified commitments. Bricker (2020) gives the standard contemporary taxonomy of how Lewisian worlds individuate. Against the concrete variant stand the abstract or ersatz realists: Plantinga (1974b) defends worlds as maximal states of affairs; Stalnaker (1976, 1984) treats worlds as maximal properties; Adams (1974, 1981) as maximal consistent sets of propositions; Kripke (1980) operates with primitively stipulated worlds rather than discoverable ones. Van Inwagen (1986) presses the central internal critique: the plurality is ontologically exorbitant without being explanatorily adequate. Rosen (1990) develops modal fictionalism as an explicit alternative: the plurality as useful fiction, not reality. Armstrong (1989) pushes combinatorialism: possibilities are recombinations of actual constituents, no alternative universes required.

The present reply sits closest to Armstrong's combinatorialism in rejecting the concrete plurality, and adds what combinatorialism alone does not specify: which structural roles any recombination must preserve. Why they cannot be recombined apart is supplied not here but by the cross-entailment among the three roles ([§2.4.8](<2.4.8 Exchange Requires Physicality.md>), [§2.6](<2.6 Triconditionality of Nature.md>)): they are not distinct existences for recombination to separate.

Modal Realism presses directly against the necessity claim of the argument. What [§2.8.5](<2.8.5 Necessity of Nature.md>) establishes is □(T∧S∧Φ): in every world within the fixed global domain of real possibility, the structural Conditions obtain. S5 is earned from the fixed-domain reading of real possibility ([§2.1](<2.1 The S5 Pipeline.md>)), not assumed as an axiom. Transition Closure is a narrower result about the onset of Change under structural accessibility; it is not an independent derivation of proposition-wise S5. If possible worlds are concrete universes, the question is what every concrete universe in that global domain contains. Lewis's plurality is the most permissive ontology of possibility ever defended: if any consistent-sounding description individuates a concrete world, worlds without structure might be among them. The argument's necessity claim is false if even one concrete world lacks T, S, or Φ. (ET) (the Exhaustion-of-Existence claim, that T, S, and Φ exhaust the forms of real existence) is false on the same condition.

A clarification before the moves. The dispute is not with Lewis's counterfactual semantics or with the usefulness of possible-world talk. The question is whether the concreteness criterion Lewis himself requires (the feature that distinguishes Lewisian realism from ersatz alternatives) permits radically sparse worlds to qualify as concrete. The move comes at several resolutions: the bare sparse-world move and its sharpened recombination form, the isolation-thesis variant, and the primitivist fallback. The space they canvass is the space Lewisian realism can occupy. The replies argue that each collapses concreteness back into structure before the plurality is assembled.

*First.* The sparse-world move holds that among the plurality there is a world w′ containing a single unchanging state: no succession, no spatial extension, no causal activity. Such a world is conceivable, and the move needs conceivability of a coherent description to entail concrete existence of the corresponding world. w′ contains no T, no S, no Φ, and it concretely exists.

For Lewis, worlds are maximal sums of spatiotemporally interrelated things, with worldmates unified by the relevant natural external relations. This gives Lewisian worlds a spatiotemporal criterion where such relations obtain, but it does not by itself prove that every world contains both temporal succession and spatial extension. A sparse or changeless world remains a live test of the book's independent type-level arguments. The present argument need not claim that every abstract representation of a world has those types; it claims that a concrete world proposed as a real change-realizer cannot lack them. A world with no temporal succession has no internal change that could individuate one world-state from another, which means no structural fact distinguishes “world w′” from “no world.” A world with no causal persistence has no bearer across which content could be sustained. A world lacking all three is not a sparsely furnished concrete world. It is not a concrete world at all. Lewis's own concreteness criterion forecloses the sparse-world move before the plurality is even assembled.

*The sharpened form: recombination.* The sparse-world move has a sharper version that does not empty the world at all: Lewis's principle of recombination. The principle permits extensive recombination of distinct existences, subject to its own constraints; it does not license every arbitrary description as a world. Recombination does not need the empty world; it needs only a selective deletion of what the Humean treats as distinct. Take a spatiotemporally extended world and deny necessary connections between its distinct local states; the resulting Humean mosaic retains Time and Space while rejecting a necessary productive connection between distinct existences. The issue is whether the mosaic can retain the structural work the present account assigns to Φ without thereby retaining Φ under another description.

The reply must not answer it by saying the mosaic "has no bearer," since whether a world requires a persisting bearer is precisely what the Humean denies; to assert it here would beg the question.

The reply turns instead on what the mosaic already grants. A mosaic is a distribution of local states across a spatiotemporal manifold: Lewis (1986b, pp. ix–xvi), introducing Humean supervenience in *Philosophical Papers, Volume II*, exempts the spatiotemporal relations from it and takes them as primitive, so the manifold is conceded, not constructed. The manifold grants differentiation and spatiotemporal arrangement. It does not follow merely from exclusion or Best-System regularity that a productive cross-interval causal operation exists: the Humean denies exactly that inference. The sharper question is whether the mosaic realizes Φ's broader bearing or continuity role without accepting productive necessary connections. A regular mosaic may remain a substantive rival at the type level rather than collapsing into ∅.

*Second.* The isolation thesis presses from a different angle. Lewis's worlds are spatiotemporally isolated from one another: no causal or spatiotemporal connections between them. A world in the plurality need not be internally rich; it needs only to be isolated from other worlds. A single unchanging state, isolated from all other such states, qualifies as a world by isolation alone.

Lewisian worlds are isolated in the sense that no spatiotemporal relations connect their inhabitants; isolation is not an additional between-world relation requiring a common surrounding manifold. The thesis therefore does not establish any particular world's internal richness. Whether a sparse candidate qualifies as a world turns on Lewis's worldmate criterion and the candidate's contents, not on reifying non-connection as a structural relation. The isolation thesis is a structural criterion applied to structured worlds, not an alternative to structure.

*Third.* The primitivist version goes boldest. Being a world is a primitive fact, irreducible to any further ontology. Worldhood is fixed by the modal role 'world' plays: as the primitive truthmaker for modal claims. This is a coherent rival semantic proposal, but it carries a cost: it declines a constitutive account of what makes a world concrete or a genuine realizer of change.

The present argument cannot close primitivism by retorsion alone. At most, it can show that any primitive world introduced as a concrete universe or as a realizer of change inherits the relevant role- and type-level burdens. A primitivist who treats worldhood as primitive while refusing those burdens has replaced structural explanation with an additional primitive. That is a theoretical cost, not a contradiction.

A further Lewisian pressure targets the Modal Identity directly rather than the concreteness of worlds. Lewis's counterpart theory denies strict trans-world identity. What you would have been had you taken the other job is your counterpart in another world: qualitatively similar, numerically distinct. The Modal Identity of [§2.6.6](<2.6.6 Modal Identity.md>) (□(◇C ↔ (T∧S∧Φ)), where ◇C is the possibility of change) appears, under counterpart semantics, ambiguous between a claim about the same T, S, and Φ across worlds (requiring trans-world identity Lewis denies) and a claim about qualitatively similar structural roles in each world (a weaker claim counterpart theory permits but insufficient to ground the necessity the argument needs). Either the Modal Identity assumes identity Lewis rejects, or it retreats to similarity that cannot carry the argumentative weight.

The dilemma dissolves at what the Modal Identity of [§2.6.6](<2.6.6 Modal Identity.md>) actually asserts. The Modal Identity does not claim a numerically identical token of T, S, or Φ recurs across worlds in the way ordinary individuals would have to for strict trans-world identity. It claims any world containing change contains the structural *roles* change requires: whatever plays Time's role in w and whatever plays Time's role in w′ are both instances of a single role-type. Role-type identity is not the kind of trans-world identity counterpart theory forecloses. Counterpart theory denies strict identity of individuals because individuals are, on Lewis's picture, worldbound particulars. Structural roles are not particulars; they are types any particular must instantiate to be the kind of thing it is. Lewis (*On the Plurality of Worlds*, [§1.5](<1.5 Existence.md>)) is explicit that properties are classes of their actual and possible instances: an across-world specification counterpart theory permits for types even as it forbids it for tokens. A structural role meets that specification directly: “whatever plays Time's role” picks out the class of its actual and possible role-players, which is just what a property is on Lewis's account. The role-type is therefore not a trans-world individual smuggled past counterpart theory but an abundant property in Lewis's own sense: identified, as every Lewisian property is, by its actual and possible instances across the plurality. The Modal Identity operates at the level Lewis's own semantics already allows, and the structural roles fit the property-class regimentation rather than being exempted from it. A second counterpart-theoretic pressure, aimed at the transfer principle rather than at the Modal Identity, runs through the chained-origin cases of Chisholm, Chandler, and N. Salmon; it is engaged at [§4.4.11](<4.4.11 Chisholm’s Paradox Chained Origins.md>).

A kindred move drops Lewis's concrete realism for Stalnaker's (1976) moderate realism: possible worlds are abstract maximal ways the world could be, not concrete alternative universes. The abstract-realist variant is closer to the Platonist challenge of [§4.2.4](<4.2.4 Platonism.md>) and is answered there. The reply in the modal-realist vocabulary: abstract maximal ways can be distinguished and compared, directly supporting only a thin difference-role. They need not thereby instantiate temporal succession, spatial extension, or causal persistence. The richer roles apply when a way represents or realizes a concrete change-world, not merely because it is an abstract modal surrogate.

*What converges.* Each form collapses concreteness back into structure before the plurality is assembled. The sparse-world move founders on Lewis's own concreteness criterion: a world with no spatiotemporal structure is not a sparsely furnished concrete world but no concrete world at all. Its sharpened recombination form is not closed by definition: the mosaic's conceded manifold already grants differentiation and arrangement, and whether Best-System regularity can discharge Φ's bearing role without productive connections is the type-level question the mosaic remains answerable to. The isolation thesis is itself a structural relation: isolation is a spatiotemporal concept, and worlds can only satisfy the isolation criterion if they have spatiotemporal structure to be isolated with. Primitivism about worldhood does not escape the structural account so much as decline it: the refusal replaces structural explanation with an additional primitive, a cost the position carries rather than answers.

*A stronger reply: the unity of the frame.* The replies so far grant Lewis his plurality and show only that each member of it must instantiate the structure; a bolder reply presses the count itself, and it stands apart from the rest because it reaches further and leans on a premise Lewis is entitled to refuse. A plurality is a plurality only if its members are genuinely many, and genuine two-ness is not bare: for two concrete totalities to be two rather than one totality described twice, there must be a real interval in which their non-identity registers — an interval something could cross ([§2.4.7](<2.4.7 Distinction Requires Spatiality.md>), the Constitutive Premise; [§2.4.1](<2.4.1 Constituting Modal Structure.md>), its world-level form). Lewisian worlds are by definition isolated, with no spatiotemporal relation and nothing crossable between them, so the distinctness they require is exactly the kind [§2.4.7](<2.4.7 Distinction Requires Spatiality.md>) declines to grant: a difference with no interval, which is either relational after all — a shared structure, hence one connected order, and isolation is lost — or a bare thisness, “a label without an interval,” which does not make two. Isolation is the absence of a separator, not a mode of separation; “two isolated concrete worlds” asks the cardinal predicate to grip where nothing gives it purchase. The same pressure shows in the very act of pointing: to single out a world as *that* one is to set it off from *this* one, and this-and-that is here-and-there in other clothes. “That world” says “not here,” and “not here” asks after a where — either a location standing off from this one, which is a relation and undoes the isolation, or no where at all, in which case “that” has singled out nothing. The plurality cannot be so much as indicated without borrowing the frame it was meant to exceed.

A deeper tightening follows. The primitivist might concede the demonstrative point — that "that world" borrows the here-and-there it was meant to outrun — and insist instead that bare thisness simply is, at the level of being, prior to any pointing or description. The question that move cannot answer is what it is. A world must be a something: it must carry enough determinate content to be a world rather than its own absence. Bare thisness strips every qualitative, relational, and structural feature by design — that is what "bare" means. What remains when all content is gone is ∅, not a minimally furnished concrete world but the null case. "Bare thisness exists" and "nothing exists" are, on every dimension that could distinguish them, the same description. A posit indistinguishable from ∅ has not located bedrock below structure; it has dissolved into the null case — which is the absence of a world, not an instance of one.

Stated precisely, what this reaches is not the numeral "exactly one world" but the unity of the frame. Reality is not the winner of a headcount among possible many; it is a unity-of-structure — the one frame any configuration must instantiate, beyond number rather than one of a kind ([§6.2.2](<6.2.2 Unity.md>)). “One,” said of Nature, is not a cardinality but that unity: positions within the one logic of here-and-there can be multiplied without end, but not the logic of here-and-there itself, which is no particular admitting duplication but the frame within which any “two” is sayable. On this reading the plurality is not outweighed but mis-formed — a cardinal count run at the one level where the cardinal predicate finds no grip.

The candor the rest of the book keeps is owed here too. This is not a deductive refutation of a determined primitivist. Lewis can plant precisely on the fault line [§2.4.7](<2.4.7 Distinction Requires Spatiality.md>) marks: he can hold the numerical distinctness of concrete totalities to be primitive — needing no interval and no ground — and the reductio does not move him, because its load-bearing premise is the one he denies. What the reply secures against him is not formal contradiction but a convergent exposure: bare thisness dissolves into ∅, the absence of a world rather than an instance of one, and the cost of maintaining the posit against that dissolution is not confined to the cross-world case: the same bare thisness he plants on can no more make one being one across a change, absent continuous carrying, than it can make two worlds two absent an interval ([§2.4.1](<2.4.1 Constituting Modal Structure.md>)). Nor can he discount that cost by making the distinctness merely numerical — the bare non-identity of two from three — for that is how abstract objects are told apart, and abstractness is the one price Lewis cannot pay: concreteness is what separates his realism from the ersatz alternatives he wrote against. He wants the numeral’s economy and the world’s concreteness together — a two with a world hung upon it — and they do not combine, since the entire content of concreteness is the here-and-there that a bare numeral forgoes ([§2.4.1](<2.4.1 Constituting Modal Structure.md>); [§4.2.4](<4.2.4 Platonism.md>)). His intervalless plurality is a positive existential posit with no access and no causal trace, carried for a modal-semantic payoff the structural account already supplies from a ground that is independently necessary ([§2.8.5](<2.8.5 Necessity of Nature.md>)). And the terrain the unity reading stands on is not an ad hoc anti-Lewis axiom but the oldest treatment of the one and the many — Plotinus’s source of number that is itself beyond number, mathematical structuralism, Spinoza’s single substance. The plurality remains sayable; what it has lost is its cheapness: distinctness-without-relation is the least defensible of the position's commitments, and the unity of the frame is what one reaches the moment that commitment is refused.

The cost ledger carries one more line, and it is quantitative. Grant the primitivist his bare distinctness, and the plurality still owes an answer no positive existential posit gets to waive: how much of it is there? Lewis’s own machinery cannot settle the question. Forrest and Armstrong (1984) showed that recombination, applied without restriction to the totality of worlds, generates a world containing duplicates of all the worlds — a world bigger than any world, itself included — so neither the aggregate nor the set of all worlds survives the principle’s own closure. Lewis’s reply (*On the Plurality of Worlds*, [§2.2](<2.2 Cartesian Certainty.md>)) restricts recombination by the proviso the principle already carries in its statement ([§1.8](<1. Groundwork.md>) of the same work), “size and shape permitting,” a qualification whose content he leaves unspecified; Nolan (1996) argues the restriction is unmotivated on Lewis’s own terms, and the alternative he defends, recombination unbound with more possibilia than any set can hold, concedes the point at issue here: the plurality has no determinate size. Either way the count never closes. A finite tally of concrete totalities would be arbitrary — nothing in the theory could say why that many and no more — and the infinite alternative cannot be stabilized at any cardinality. A posit whose quantity is in principle unanswerable carries exactly the mark the unity reading predicts: number failing at the level of totalities. What looks from inside the theory like a bookkeeping embarrassment is, read structurally, the same finding the interval argument reached from outside — there is no fact of how many, because how many is not a question the frame can answer about itself.

The shape of the mistake can be put more plainly. Each Lewisian world is internally rich — intervals throughout, a full spatiotemporal interior, exactly like the interior of a fiction, which stipulates its own distances freely. What carries no interval is the relation *between* worlds. That relation is a seam — world-to-world as fiction stands to reality — and every seam we have uncontested access to is interval-free precisely where it is non-concrete: there is no distance from Sherlock Holmes to Hamlet, not an unknown distance but no such fact. The photograph in your hand sits a foot away, while the person it pictures, held now as pictured, is at no distance from you at all; the only way to recover a distance is to switch back from the representation to the living worldline — from the seam to a concrete interior. Lewis is thus a concretist about each world and, without owning it, an ersatzer about the many: he imports the interior's concreteness across a seam that bears none of concreteness's marks. His plurality is a set of concrete relata related as if they were non-concrete. And the intuition that makes the picture feel forced — that the worlds are *obviously* many — leans on distinguishability, which is downstream of the structure and confers no actuality of its own: that two worlds can be told apart no more makes them two concrete existents than telling Holmes from Hamlet makes either one a man. The arrow runs from the Conditions to distinguishability, never back.

*On the Plurality of Worlds* defends concrete realism against what Lewis called “the incredulous stare”: the reaction he expected from any reader encountering the view for the first time, and which he thought no sufficient response to a working modal semantics. The reaction it provoked was not confusion about the view's coherence but a genuine ontological concern: one Lewis acknowledged and thought the modal semantics outweighed. What Lewis left behind is not the plurality but a diagnostic: any modal ontology powerful enough to do the work has to specify what makes a world a world, and whatever does the specifying instantiates the structure the argument names. Ersatz worlds individuate by property or proposition; concrete worlds individuate by spatiotemporal aggregation. Either specification is a structural fact. What the plurality purchased in modal expressive power it paid for in ontological commitment, and the ontological commitment, examined for what it requires, confirms the structural conditions the argument derives.


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← [4.4 Modal Variants and Extensions](<4.4 Modal Variants and Extensions.md>) | [4.4.2 Linguistic Ersatzism](<4.4.2 Linguistic Ersatzism.md>) →
