This section supplies the proof's input, not its conclusion. The S5 pipeline of [§2.1](<2.1 The S5 Pipeline.md>) closed with a conditional and no antecedent discharged: whatever is possible is necessarily possible (the Necessary Possibility Theorem, [§2.1.10](<2.1.10 Necessary Possibility.md>)). Nothing has yet been shown to be possible. The theorem needs exactly one input: ◇C, that change is really possible. And change is not merely possible but actual, since the reading of this sentence instantiates it. Nor is the input deniable. Trying to deny change performs it.

> [!premise]
> **Cartesian Certainty** · **P2** · *Premise 2*
>
> Change is really possible. No denial can escape it: the act of doubting that anything changes is itself a change, from not-doubting to doubting. ◇C.

The certainty is Cartesian in a precise sense. The witness is the *Cogito*'s structural shadow: any attempt to doubt that change occurs is itself a change, a transition from not-doubting to doubting, performed across a real interval, hosted by a persistent doubter. The doubter here is a functional role: the state constituting doubt is structurally distinct from its absence, and that structural difference is the change the witness requires. The doubt refutes itself in its own performance: no denial of change can be completed without instantiating it. That is Cartesian certainty for the possibility of change, in one exact grade: the performative inescapability of the structural transition, self-defeating to deny, not the phenomenal indubitability the term can suggest. "Cartesian" marks the *Cogito* on the performative reading taken up at [§2.2.1](<2.2.1 Change Is Actual.md>), not an introspective luminosity of the doubting.

Two limits hold that grade in place. Phenomenal character is not the datum, and the witness does not depend on it (that pressure is taken up at [§4.3.2](<4.3.2 Eliminativism and Illusionism.md>)). And the change instantiated is intrinsic state change of the doubting system, not duration of time or causal direction per se: what the witness establishes is that change is sufficient to instantiate the structural Conditions, not that temporal structure cannot proceed without intrinsic change, which is Shoemaker's freeze argument and is engaged at [§4.2.2](<4.2.2 Shoemaker's Time Without Change.md>).[^2-2-0-change-witness-ch4]

The performative catch is the *Cogito*'s shape redirected: *Cogito Ergo Muto*. The argument is given in full at [§2.2.1](<2.2.1 Change Is Actual.md>), where change is shown to be actual and certain at three depths — empirically, performatively, and structurally — under the *Cogito*-style closure of [§1.3](<1.3 Change.md>) that no skeptical scenario can undermine.

The input then does its work in two directions. First, it does not lapse once secured: fed into the Necessary Possibility Theorem ([§2.1.10](<2.1.10 Necessary Possibility.md>)), ◇C carries to its necessitated form, □◇C: what is possible is possible in every world constituted by modal structure. Second, the certainty reaches past experience to whatever grounds it: the extension from the act of doubting to any ground that could host it is carried at [§2.2.2](<2.2.2 Actuality's Reach.md>) by three independent lines — level-invariance, the Triconditional Cross-Entailment, and the Encoding Dilemma, whose result, Constitutive Instantiation, is proved at [§2.6.7](<2.6.7 Triconditional Cross-Entailment.md>).

The argument extends a defended tradition. (Hintikka, Jaakko, 1962) read Descartes' *sum* as performed rather than inferred: the *Cogito*'s force lies in the fact that any denial of one's existence re-establishes it in the act of denying. (Apel, Karl-Otto, 1980) and (Habermas, Jürgen, (1983) 1990) extended the move to the presuppositions of argumentation itself. (Stroud, Barry, 1968) and (Taylor, Charles, 1978) formalized the general pattern: an X is unavoidable if every possible denial of X requires X for its formulation. What is new here is the target: not the presuppositions of reasoning in general but the structural conditions of any state of affairs being the case, regardless of whether anyone argues about it.

Stroud's own objection sharpens the stakes. Transcendental arguments, taken alone, establish only what must be presupposed for experience or assertion to occur. What entitles the move from a fact about the act of denial to a conclusion about mind-independent reality? Nothing — so long as the performative line stands alone. The reply is a pairing. The performative line (this section) shows that the act of denial or conceiving is itself structurally conditioned: anyone running the denial uses what it rejects. The constitutive-definition line ([§1.4](<1.4 Three Conditions.md>)) carries the metaphysical claim: the Conditions are what it is for any state of affairs to be the case — constitutive of its obtaining, not its subject matter. Neither move alone closes the gap. Cognitive performance alone does not defeat the ideal conceivability of a structureless scenario, and the constitutive definitions alone leave the performance certainty unanchored. The two together do.[^2-2-0-cogito-illusion-ch4]

[^2-2-0-cogito-illusion-ch4]: [§4.3.2](<4.3.2 Eliminativism and Illusionism.md>) engages the Ch 4 objections that the cognitive performance the *Cogito* presupposes is itself illusory or eliminable; [§4.3.1](<4.3.1 The Hard Problem of Consciousness.md>) takes up the related objection that consciousness as substrate stands outside structural exhaustion, the hard problem of consciousness. The input secures the possibility of change without itself answering the hard-problem pressure, which is carried forward rather than discharged here.

[^2-2-0-change-witness-ch4]: The [§4.2](<4.2 Time, Change, and the Changeless.md>) cluster engages the Ch 4 objections targeting the change-witness itself: [§4.2.1](<4.2.1 The Changeless Ground.md>) takes up changeless-ground accounts that would refuse the witness, and [§4.2.2](<4.2.2 Shoemaker's Time Without Change.md>) handles Shoemaker's argument that the temporal structure can hold without change.


- [2.2.1 Change Is Actual](<2.2.1 Change Is Actual.md>)
- [2.2.2 Actuality's Reach](<2.2.2 Actuality's Reach.md>)
- [2.2.3 Witness's Reach](<2.2.3 Witness's Reach.md>)


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← [2.1.10 Necessary Possibility](<2.1.10 Necessary Possibility.md>) | [2.2.1 Change Is Actual](<2.2.1 Change Is Actual.md>) →
