The Necessary Possibility Theorem has two readings because the fixed domain of real possibility can be indexed in two ways. The theorem itself is one result: all modal evaluation ranges over the same complete domain W of real possibilities (§[§1.2.1](<1.2.1 Possibility.md>), 2.1.4–2.1.5). It does not rest on a separate w′ derivation or on Transition Closure.

*Modal Persistence, the diachronic reading.* A later time does not create a new domain of real possibilities. What becomes locally achievable, ceases to be locally achievable, or is never actualized concerns occasions and configurations; it does not add or remove members of W. A possibility may lack an occasion at a time without lapsing in modal status.

*Modal Invariance, the cross-world reading.* The same point holds across worlds. A witness to ◇P is a member of W, and every world evaluates real possibility over W. Thus ◇P → □◇P; if no member of W witnesses P, ¬◇P → □¬◇P.

The two readings are not two causal stories about structural Conditions changing or persisting. They are two indices of one global semantic fact: temporal changes and world-relative accessibility relations do not replace the complete domain that real possibility quantifies over.

Plantinga -(Plantinga, A., 1974) develops modal invariance for essentialist claims about individuals. The present theorem generalizes the result to real modal status and grounds it in the fixed global domain of possibility. A critic may instead use a world-relative modality with varying accessibility horizons; that is a different operator, not a counterexample within ◇.

*What binds.* The modal architecture is globally stable: whatever modal status a proposition bears in the complete domain W, that status is invariant under evaluation at any member of W. Local opportunity remains local; real possibility is global.[^2-1-7-two-readings-ch4]

[^2-1-7-two-readings-ch4]: The global and relative readings of modality are pressed in Chapter 4: Williamson ([§4.4.6](<4.4.6 Necessitism.md>)), Lewis ([§4.4.1](<4.4.1 Modal Realism.md>)), modal collapse ([§4.4.9](<4.4.9 Modal Collapse Objection.md>)), and the source-of-possibility question ([§4.1.10](<4.1.10 The Source of Possibility.md>)).


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← [2.1.6 The Transition Closure](<2.1.6 The Transition Closure.md>) | [2.1.8 Candidate-Ground Convergence](<2.1.8 Candidate-Ground Convergence.md>) →
