The Null State resists statement, but it does not resist refutation. Two inferences settle it (one modal, one temporal) and both rest on the diagnosis already in hand from [§2.7.1](<2.7.1 Null State (∅).md>): ∅, as the joint absence of T, S, and Φ, cannot host any obtaining, since to host an obtaining is to sustain a structured state of affairs, and ∅ is precisely the absence of the conditions a structured state of affairs requires.

> [!info]
> **Core concept.** The null state—nothing whatever, the total absence of time, space, and persistence—resists being stated, but it doesn't resist refutation. Here's the clean version. If the null state held, nothing could obtain, since obtaining anything takes a structured state of affairs and the null state is precisely the absence of what that requires. But something does obtain, and whatever obtains is possible. So the null state doesn't obtain—and since the possible is necessarily possible, it obtains at no world. A temporal version follows: if nothing could ever come from the null state, and something is here, then the null state was never the starting point. Nothingness isn't an empty stage that something later walks onto.

> [!argument]
> **Incoherence of ∅** · *The Modal Form*
>
> 1. If ∅ is a possible world, ∅ is an evaluation point: a world at which claims, modal claims included, can be true or false (◇∅ → ∅ is an evaluation point).
>
> 1. Being an evaluation point requires sustaining a structured state of affairs — holding contents one way rather than another ([§2.1.5](<2.1.5 The S5 Bottleneck.md>)).
>
> 1. ∅, the joint absence of T, S, and Φ, sustains no structured state of affairs and so is not an evaluation point, by definition ([§2.7.1](<2.7.1 Null State (∅).md>)).
>
> 1. Therefore ∅ is not a possible world, by modus tollens on steps 1 and 3 (¬◇∅).

The argument targets ¬◇∅ directly rather than reaching it from a local, world-relative result. It does not move from ∅'s lacking some particular obtaining at a candidate world to a modal verdict reached *at* that world, a move that would already need ∅ to be an evaluation point before the argument has shown any such point exists. Instead, step 1 fixes what any possible world must be able to do, and steps 2–3 show ∅ cannot do it. Both premises hold unconditionally: step 1 by what a possible world *is*, and step 3 by what ∅ *is*, wherever the question is raised.

One residual position closes quickly. The strong Kantian relocates the roles to the transcendental subject, but a subject that contributes causally structured succession to experience must itself undergo causally structured transitions to contribute them. Relocating the Conditions does not remove them from the ontological inventory; it confirms them at a different level. The modal-fictionalist relocation is taken up at [§3.3.3](<3. Convergence.md>).

A deeper objection leaves the premises untouched and attacks the inference. Both forms use classical reductio — modus tollens on lines 1 and 3 in the modal case, on lines 2 and 3 in the temporal — and a determined opponent can try to keep ◇∅ open by revising the consequence relation. The revisions differ. A dialetheist may accept ◇∅ ∧ ¬◇∅; that challenges exclusivity without falsifying the disjunction ◇∅ ∨ ¬◇∅. A paraconsistent logician may deny that the contradiction licenses explosion, while an intuitionist may reject the classical closure used here. The reply does not refute those logics in general or derive explosion from the contradiction. It asks the narrower question whether any such inferential practice supplies a model of ∅. To hold the formulas apart, order the steps, and sustain an evaluation is to instantiate distinction (S), succession (T), and a medium of persistence (Φ). Either the proposed rescue is a genuine inferential practice, in which case it cannot itself exemplify the joint absence of the Conditions, or it is not a practice at all, in which case it supplies no model of ∅. This establishes an act-side limit on the rescue; it does not by itself force the revisionist to accept the book's object-level classical logic. The wider dispute over whether structural enactment settles a positive metaphysical thesis remains open in the form [§5.3.4](<5.3.4 Madhyamaka Emptiness.md>) marks. The temporal leg is narrower still: the revisionist performs the token inference in time, so that token cannot exemplify timeless absence.

> [!info]
> **Natural worry.** A determined opponent leaves the premises alone and attacks the logic instead: revise the rules—accept the contradiction, block the explosion, reject classical closure—and maybe nothingness stays open. The reply is that the rescue refutes itself in the stating. To run any inference at all, even a revised one, is to tell one claim from another (distinction), order the steps (succession), and sustain a medium across which it holds (a bearer). The defending practice enacts the three conditions in the very act of turning them against themselves. Either it's a real inferential practice, and so instantiates the structure, or it's no practice at all and states nothing. And it's performed in time, so the temporal leg is conceded outright.

The temporal half is best stated as a scope reductio rather than as a persistence claim: saying that ∅ obtained *at a past time* already places it within Temporality, which ∅ excludes.

> [!argument]
> **Incoherence of ∅** · *The Temporal Form*
>
> 1. Let H∅ mean that ∅ obtained at some past time t.
>
> 1. For t to be a past time at all is for t to stand in succession-relations — Temporality-facts at t. So H∅ entails T at t.
>
> 1. By definition, ∅ is the joint absence of T, S, and Φ; for ∅ to obtain at t is for Temporality to be absent at t. So H∅ entails ¬T at t.
>
> 1. Therefore H∅ entails both T and ¬T at the same evaluation point t. So ∅ obtained at no past time: ¬H∅.

This is the *Parasitic Negation Lemma* ([§2.1.5](<2.1.5 The S5 Bottleneck.md>)) instantiated to the joint case: the absence of all three structural domains hosts no obtaining, and obtaining is given. In plain terms, nothingness is not an empty starting point from which something later appears; had ∅ ever obtained, nothing could have followed from it, and since something obtains, ∅ was never the state of Reality.

The two inferences converge on a single result.

> [!lemma]
> **Incoherence of ∅** · **L6** · *Lemma toward ∅ Reductio*
>
> The Null State is not a coherent alternative to structure: it cannot be the case at any possible world, and it never obtained at any past time. ¬◇∅ ∧ ¬H∅.

The lemma does not rest on this argument alone. Chapter 3 reaches it again from independent directions: each of its convergent lines closes ∅ on its own, and the purified null-state backstop at [§3.2](<3.2 Triconditional Necessity Positive Account.md>) re-grounds the point on the construction line (*Something is the case*), overdetermining both conjuncts established here.


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← [2.7.1 Null State (∅)](<2.7.1 Null State (∅).md>) | [2.7.3 PSR Regress](<2.7.3 PSR Regress.md>) →
