Even a reader who refuses every construction in [§3.2](<3.2 Triconditional Necessity Positive Account.md>) has one move left: deny the conclusion outright. Grant nothing about how the Triconditions are built: simply assert that □(T ∧ S ∧ Φ) is false. This is the strongest-looking escape precisely because it engages no premise; it concedes no step, and so seems to expose none. But the denial is not free. To deny anything is to *perform* a propositional act, and a propositional act already runs on T, S, and Φ, so the denial instantiates exactly what it denies.

> [!argument]
> **The Self-Refutation** · *from the performance of any denial to Triconditional Necessity*
>
> 1. Any denial of □(T ∧ S ∧ Φ) is a propositional act.
>
> 1. Any propositional act requires T, S, and Φ as its conditions of possibility.
>
> 1. So any denial of □(T ∧ S ∧ Φ) instantiates T ∧ S ∧ Φ.
>
> 1. This holds in every world where a denial is so much as formulated (no principle of sufficient reason assumed).
>
> 1. A world with no denier is untouched by the performative argument. Its silence does not imply that it lacks any Condition, and a denier-free world cannot be identified with ∅ merely from the absence of a tokened denial.
>
> 1. So the line establishes T ∧ S ∧ Φ wherever a denial or inference is performed. Cross-world necessity requires the separate silent-world bridge identified at §[§3.1.3](<3. Convergence.md>) and 3.5.4.

*Why the act carries the Triconditions.* Step 2 is the load-bearing one, and it earns its keep the same way its siblings do. To deny anything (even "□(T ∧ S ∧ Φ) is false") is to *perform* the denial, and the act of denying already runs on all three conditions. It moves from not-having-denied to having-denied: one state, then another, which is just temporal passage (T). It marks the denied content off from what is affirmed in denying it: a distinction drawn, which is structure (S). And it is borne by some thinker or token that sustains it as the very act it is, a bearer that holds the act together (Φ). So the denial does not merely *mention* the conditions; it *runs on* them. And a denier who took the conclusion to be false would have used, in the very taking, exactly what the conclusion asserts.

*The inferential form.* The point is broader than explicit denial. Any argument against the Triconditions must preserve premises while moving to a conclusion, distinguish those premises from that conclusion, and sustain their content across the inference. Ordered premise-to-conclusion movement instantiates T at role-resolution; distinct propositions instantiate S; retention of content across the inference instantiates Φ. The critic therefore uses the three roles even when the conclusion is framed as a counterexample, suspension of judgment, or alternative theory rather than as a denial. This strengthens the performative witness without expanding its modal reach: it applies wherever reasoning occurs and says nothing by itself about a silent world in which no inference is tokened.

*Dependency.* [§1.4](<1.4 Three Conditions.md>), [§1.3](<1.3 Change.md>) only; the performative-indispensability lineage (Hintikka, Apel, Habermas, Stroud–Taylor). No S5, no PSR. The act-side result is not counted as a freestanding proof of necessity; the silent-world limit is preserved, as [§3.1](<3.1 Necessary Possibility of Change.md>) and [§3.5.4](<3. Convergence.md>) require.


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← [3.3 Triconditional Necessity: Negative Account](<3.3 Triconditional Necessity Negative Account.md>) | [3.3.2 The Negation Trap](<3.3.2 The Negation Trap.md>) →
