With the premises in place, there remains one alternative, and the word *remains* claims more than the alternative can support. The candidate is ∅: the joint absence of T, S, and Φ.

The dissolution rests on a principle the chapter has been deploying: coherence requires change. Any coherent stance (to affirm, to deny, to suspend, to consider) is a structured cognitive act, and a structured cognitive act has the form of what it is supposed to be alternative to. The *Cogito* of [§2.2.1](<2.2.1 Change Is Actual.md>) was one instance: thinking coherently, even thinking *I am being deceived*, deploys distinction, succession, and persistence. The same diagnosis runs at full scope here, self-contained within this chapter: ∅ cannot be coherently entertained, because the entertaining itself is among the things the Conditions make possible.

Five grades of *nothing* need to be kept apart. (i) *Perceptual void*: no sensible objects to a perceiver. (ii) *Cognitive blank*: no phenomenal content to a subject. (iii) *Quantum vacuum*: the lowest-energy state of a quantum field, fully law-governed. (iv) *Abstracta-only world*: no concreta but a residue of numbers, sets, or propositions. (v) *Absolute structural absence*: no T, no S, no Φ. The first four are coherent but ontologically rich, and each fits inside structure rather than outside it: grades (i)–(iii) instantiate at least two of the three Conditions, while grade (iv) depends on them in the abstraction-and-hosting sense of [§2.6.12](<2.6.12 Necessity's Nature.md>) (the Platonist alternative is engaged at [§4.2.4](<4.2.4 Platonism.md>)). Only the fifth is ∅. (Pizzi, David, 2025) charts a parallel taxonomy culminating in *Absolute Nothingness*; ∅ is the same target named from the structural side rather than the existential side. The argument that follows operates only on grade (v); the weaker grades are not in dispute and not in scope.

Try to think of nothing. Not nothing in the casual sense: really nothing. You cannot think of it as an empty container; empty and container already require Spatiality and Physicality. Strip the picture. No motion, no shape, no weight; no sound, smell, or touch. Even without definition, the word *nothing* describes too much. *Nothing* is a Physicality-domain word: *no* + *thing*, the absence of a thing where a thing might have been. But Temporality and Spatiality are not things, and ∅ is not the absence of a thing. Natural language gives the Triconditions three parasitic negations (*nothing*, *nowhere*, *never*) each leaning on the other two domains still running; none of them, singly or stacked, reaches the triconditional collapse (below). The form is uniform: ¬∃ over a domain, which presupposes the domain to be specified at all ([§2.1.5](<2.1.5 The S5 Bottleneck.md>), Parasitic Negation Lemma). The negation of change shares the form, *changeless*, and the same limit: it cannot stand outside what it negates. A state that can only be described by what it is not, and not, in truth, even by that. The only way to say it:

> [!definition]
> **Null State** · *Definition*

The definition is as full as what it refers to. Where ∅ stands, nothing lies below. Without change, nothing could possibly be otherwise.

*The impossibility argument.* Any state purporting to be ∅ cannot host the obtaining that is given: to host an obtaining is to sustain a structured state of affairs, and ∅ is precisely the absence of the conditions any structured state of affairs requires. That this renders ∅ not merely unstatable but impossible (incapable of obtaining at any world, and never the case at any past time) is established formally next ([§2.7.2](<2.7.2 Incoherence of ∅.md>)).

*What is precluded.* The same impossibility extends to candidate grounds specified as actuality without conditions. Take the position at its strongest: any proposed necessary ground claimed as actuality with no further actualizing to do (no unrealized potentiality, no succession, no distinction, no exchange) is presented as transcending rather than refusing actualization: source-side of the actualization relation (fully generative) rather than its zero (fully empty). Granted at full strength, the present reading still lands. The Triconditions running together *are* what actualization *is*. Stop it and there is no higher actuality; there is no succession, no distinction, no exchange. Which is to say: ∅. Actuality requires the conditions on which actualizing depends; a candidate ground specified as actuality-without-conditions is not a higher actuality but ∅ under another description. The preclusion is stated here in preview; its formal discharge is Theorem 7 ([§2.8.6](<2.8.6 Exclusivity of Nature.md>)), on the Triconditional Cross-Entailment ([§2.6.7](<2.6.7 Triconditional Cross-Entailment.md>)) and the Incoherence of ∅ ([§2.7.2](<2.7.2 Incoherence of ∅.md>)). The classical theist may reply that *actus purus* differs from ∅ in being source-side of actualization rather than its zero: fully actual *qua source* rather than fully empty *qua absence*. The reply does not yet escape the reduction. Any specification of 'source-side of actualization' must import some dimension along which the source-recipient relation is articulated; if the source-recipient relation is articulated at all, the articulation runs through T (succession from source to recipient), S (distinction between source and recipient), and Φ (the persistence required for the source to *be* source across the relation). A source-side that admits *no* such articulation collapses into ∅ under another vocabulary. The fuller analogical-vs-univocal predication question (whether *actus purus* might admit a non-T/S/Φ articulation under analogical predication) is the territory of [§5.2](<5.2 Doctrines of the Divine Nature.md>) (the canonical formulation is *actus purus* in the Aristotelian-Thomist tradition: Aquinas, *Summa Theologiae* I, q.3, a.1; for contemporary defenses see (Feser, Edward, 2017)).


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← [2.7 Nothing to Consider](<2.7 Nothing to Consider.md>) | [2.7.2 Incoherence of ∅](<2.7.2 Incoherence of ∅.md>) →
