The third entry is not an independent argument but a **witness**. Its task is narrower than the preceding closures: not to range over every possible world, but to show that wherever the question is raised, its denial already exhibits the change it would exclude. It fastens ◇C to actuality wherever the question is so much as raised.

> [!argument]
> **The Performative Witness** · *from the act of denial to the actual possibility of change*
>
> 1. To deny ◇C is to perform an act: an act of denial, affirmation, or even of entertaining the question.
>
> 1. By [§1.3](<1.3 Change.md>), that act is a passage from not-denying to denying (one state, then another) and so is *itself a change*. At any world where the question is so much as raised, change is therefore *actual*.
>
> 1. From actuality, possibility follows: ◇C holds at any such world, exhibited in the very act that would refuse it.
>
> 1. This bare witness is the definitional core of what Chapter 2 packages as Cartesian Certainty (P2, [§2.2](<2.2 Cartesian Certainty.md>)), stripped of the epistemic apparatus and used here only as a ◇C-witness, never as a premise toward S5.
>
> 1. ∴ ◇C holds at every *thinking* world. The witness reaches no further on its own: the *silent* worlds (those with no thinker to token the act) are deferred to [§3.5.4](<3. Convergence.md>).

Taken alone the witness has a gap: a *silent* world (one with no thinker to token the act) is untouched by it. Section 3.5.4 records rather than dissolves that cross-world burden: without an independent bridge from role-level structure to full change-enabling types, the witness does not establish ◇C at every silent world. Sections 3.2.6 and 3.3.4 supply pressure through the ∅-floor, but they do not license identifying every ¬◇C world with ∅ merely from the witness. The full proposition-wise □◇C result therefore remains with T1 unless that additional bridge is earned.

> [!info]
> **Core concept.** Here's a neat move: you can't even deny that change is possible without proving it. To deny it—or affirm it, or just entertain the question—is to perform an act, and an act is a passage from not-considering to considering: one state, then another, which is itself a change. So at any world where the question is so much as raised, change is actual, and from actuality, possibility follows. The doubter exhibits the very thing they'd refuse, in the act of refusing it. This is a witness, not a full proof: it only reaches worlds that contain a thinker. Silent worlds, with no one to raise the question, are covered by the chapter's other two arguments.

*Dependency.* [§1.3](<1.3 Change.md>) alone; no S5, no Cartesian certainty as premise. *Structure:* transcendental / actual-instantiation witness. It delivers actual ◇C at every thinking world, and is incomplete as a standalone □◇C argument by design.


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← [3.1.2 The Unswitchable Capacity](<3.1.2 The Unswitchable Capacity.md>) | [3.2 Triconditional Necessity: Positive Account](<3.2 Triconditional Necessity Positive Account.md>) →
