The S5 principle fixes how possibility and necessity range across worlds: whatever is possible is necessarily possible, and whatever is necessary is necessarily necessary. It does not by itself say what worlds contain. This section asks the further question: what must any world instantiate for modal structure to be real?

Modal structure presupposes the structural Conditions. Possible worlds are not the ground of modal facts; they are descriptions of what Reality permits. The structural Conditions are prior to modal structure, not derived from it. What is necessary is what Reality requires. What is possible is what Reality permits.

The distinction matters. T, S, and Φ are not features located *within* modal structure, features that could in principle be subtracted to leave some thinner modal structure behind. They are what makes modal structure something rather than nothing. A natural temptation is the container picture: modal structure is a room, the structural Conditions are features inside it, so one could imagine the room without them. The container picture gets the relation backward. The structural Conditions are not contents of modal structure the way furniture is content of a room; they are what would have to be present for there to be any room at all. Vary T, S, or Φ and you do not get a different modal structure. You get none. Modal structure is constituted by T, S, and Φ, not occupied by them.

The temptation has a canonical image, and the book's habit is to run such images in reverse. Plato's prisoner takes the shadows on the cave wall for the whole of what is, then is freed into a truer order beyond them; the classical ascent leads *out* of the sensible world toward Forms that stand beyond time and space. Run the other way, the correction is not an exit. The prisoner's mistake was to take a truncated grasp of the one Reality for its whole extent, and what he ascends into is not a region beyond Temporality, Spatiality, and Physicality but the same Reality grasped without the truncation; his confinement bounded what he took to be possible, not what was. The container picture makes the prisoner's mistake one level up: it imagines an outside to modal structure as he imagines a world elsewhere, when the structure it would step beyond is what any elsewhere must already instantiate to be anywhere at all.

To introduce a ground of possibility by appealing to a possibility is to concede the possibility-space in advance. The standard theistic reply is that God is necessary: *God exists* is not a contingent matter that requires modal structure to be open at the level of God's existence. The reply shifts where the closure applies. If *God exists* is necessary, the claim *God exists is necessary* is itself a modal claim: it presupposes a modal structure in which necessity and contingency are distinguishable statuses, and a vocabulary in which *necessary* and *contingent* pick out genuinely different statuses for genuinely different propositions. Theism on this reading has to explain how God can be the source of the modal structure already presupposed by the claim of God's necessity. If theism instead holds *God exists* as contingent, the claim that God is the source of what is possible requires that *God exists* be a live option, which grants the same modal structure at a different level. Either reading faces the same pressure: the claim about God's modal status appears to use the modal structure it was meant to ground. The fuller theistic engagement belongs to Chapters 5 and 6; the point here is what the modal-structure line must carry.

The result has a neighbor in grounding theory. Schaffer's -(Schaffer, Jonathan, 2010) priority monism treats the cosmos as a whole as the one fundamental entity, with parts grounded in it rather than composing it, structurally the same claim at the modal level, arrived at from a different direction. Lowe's -(Lowe, E. J., 2006) four-category ontology reaches a categorially distinct neighbor: objects, kinds, attributes, and modes as mutually presupposing fundamentals rather than derivable from any single base — categorial equiprimordiality where the present argument runs modal equiprimordiality.

A more direct path reaches the same conclusion, taking the three Conditions in turn. For a plurality of possible worlds to be genuine — for two worlds to be two rather than one world described twice — there must be a real difference between them. Two things that share no structural relation are indistinguishable from one thing labeled twice. Real otherness requires a structural interval grounding the difference. That interval is Spatiality.

Two concrete things can differ qualitatively or be bare numerical duplicates. Qualitative difference alone does not supply an interval: red is not blue, yet nothing is traversed in passing from one to the other ([§2.4.7](<2.4.7 Distinction Requires Spatiality.md>), the Constitutive Premise). For a qualitative difference between concrete worlds to amount to their being two, it must be laid out across an interval something could cross. Duplicates that differ in no qualitative respect likewise become two only through separation. Strip away both a difference-bearing interval and separation, and nothing distinguishes the pair: they collapse into one. Black's two spheres — qualitatively identical globes in an otherwise empty symmetric universe — make the point vivid.

The remaining refusal appeals to primitive thisness: a bare haecceity distinguishing worlds without any relational ground. Where thisness is asked to distinguish worldhood or structure from no structure at all, the w′ argument separately forecloses it ([§2.1.5](<2.1.5 The S5 Bottleneck.md>)). Short of that appeal, every line to concrete otherness reinstates the interval it was meant to avoid. Mere number cannot substitute for the interval: individuation by count alone belongs to abstract objects, not concrete ones ([§4.2.4](<4.2.4 Platonism.md>); [§4.3.7](<4.3.7 Mathematical Universe Hypothesis.md>) applies the same point to Tegmark's mathematical structures).

The point cuts one way only. That two worlds can be told apart is a fact downstream of the structural Conditions — something they afford — not a resource upstream of them that could deliver concrete worlds on its own. Distinguishability is borrowed from the Conditions, not native to the worlds distinguished ([§4.2.4](<4.2.4 Platonism.md>)); it does not run backward to underwrite the existence of what it tells apart, a result drawn in general at [§4.5](<4.5 What the Rivals Carried.md>). A framework that leans on the sheer distinctness of its worlds to secure their concreteness reads the arrow backward. One residue the w′ argument does not reach is the determined concrete realist who grants each world its full internal structure and holds only the cross-world plurality primitive — distinct concrete totalities related by nothing. That position is not deductively closed; it is met on the ground of cost, where the demand for a concrete distinctness bearing none of the marks of concreteness stands as its least defensible commitment ([§4.4.1](<4.4.1 Modal Realism.md>)).

The same verdict on bare thisness carries over from the many to the one. Just as no haecceity makes two totalities two without a spatial interval, none makes a single being one across a change without continuous carrying. What keeps a being the same from one moment to the next is not a changeless core surviving beneath its alterations but the persistence of Substance carrying its content forward through Time's ordering, as argued at [§3.1.1](<3.1.1 The Changeless-Ground Dilemma.md>) and [§8.5](<8.5 Identity.md>). Bare thisness does no individuating work in either register, grounding neither the two-ness of a plurality nor the one-ness of what persists; the primitivist who rests the plurality on it leans on a posit that fails at just the point it is asked to do the work.

For those worlds to exist as genuine existents rather than labels, they must stand in some temporal relation, temporal in the abstract sense developed at [§1.4](<1.4 Three Conditions.md>): asymmetric, directed ordering, not necessarily a clock-time relation between events. The options are exhaustive: either they co-exist simultaneously (in which case they share a temporal moment and are already within Temporality's succession structure) or they do not co-exist, in which case one obtains before or after the other, which just is Temporality's asymmetric ordering. There is no third option.

Abstractist frameworks resist this by treating possible worlds as abstract objects rather than concrete existents, but only by conceding that worlds are not genuine existents, which relocates the requirement rather than defeating it: whatever hosts the abstract structure must itself be a genuine existent, and the argument applies there. The w′ argument of [§2.1.5](<2.1.5 The S5 Bottleneck.md>) closes this line independently.

For the gap between worlds to be a genuine relation (for their otherness and their temporal situation to be facts rather than labels) there must be a medium through which those relations are sustained: a relation nothing bears and nothing sustains is not a fact holding between its relata but a label laid across them, and whatever sustains a relation across an interval must itself persist as a causal relatum across it (the Cross-Interval Persistence premise, defended at [§2.4.8](<2.4.8 Exchange Requires Physicality.md>)). That medium is Physicality.

*What is established.* Modal structure does not merely contain worlds that happen to instantiate T, S, and Φ. Modal structure is constituted by them: they are the preconditions for there being a genuine plurality, a temporal situation, and a sustained connection at all. Any framework that posits a plurality of possible worlds is already operating within the structure of Reality. Not as one option among others. As the precondition the framework requires.[^2-4-1-modal-structure-constitution-ch4]

[^2-4-1-modal-structure-constitution-ch4]: Chapter 4 engages the result that T, S, and Φ constitute modal structure rather than occupying it. Plantinga's modal ontological argument supposes God's necessity to ground rather than presuppose modal structure ([§5.1.7](<5.1.7 Modal Ontological Argument.md>)), Tegmark's mathematical-universe hypothesis identifies modal structure with mathematical structure ([§4.3.7](<4.3.7 Mathematical Universe Hypothesis.md>)), Lewis's concrete modal realism makes possible worlds concrete spatiotemporal manifolds ([§4.4.1](<4.4.1 Modal Realism.md>)), linguistic ersatzism offers abstract-world surrogates ([§4.4.2](<4.4.2 Linguistic Ersatzism.md>)), and Armstrong's combinatorialism generates modal structure recombinatorially ([§4.4.3](<4.4.3 Combinatorialism.md>)).

This is Line 1 of four; Lines 2–4 follow at §[§2.4.2](<2.4.2 Structural Gap.md>)–2.4.4, four access lines converging on one constitutive premise rather than premise-disjoint proofs ([§2.4](<2.4 Structural Requirement.md>)).


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← [2.4 Structural Requirement](<2.4 Structural Requirement.md>) | [2.4.2 Structural Gap](<2.4.2 Structural Gap.md>) →
