Faced with the structural account, the classical theist has three principal responses: accept the role analysis and explain how a God defined by structural withdrawal retains determinate predicates; reject the role analysis and supply an alternative account of change, distinction, and grounding; or revise God into a temporally, relationally, or actively embedded deity. These are the three main dialectical paths the chapter evaluates.

The three horns organize the chapter's dialectical space: accept the role definitions, contest them, or revise the deity into a being that realizes them. None preserves the classical package unchanged: acceptance leaves the ∅-like specification problem, rejection incurs the burden of a coherent rival structural theory, and redefinition withdraws classical aseity. Analogy and apophasis do not create a fourth relation to the definitions; they qualify how predicates and relations are claimed to apply. Their effect is therefore assessed at §[§6.2.1](<6.2.1 Simplicity.md>) and 6.8.3. A theorist who invokes an essence-prior ground still owes the same question at a different level: how does the claimed grounding relation become determinate without merely reinstating the structural roles? The trilemma maps the available responses; it does not license treating that outstanding burden as already a contradiction.

*Horn one: Accept.* If the theist accepts the Time, Space, and Substance role definitions as the correct account of the structural preconditions for Change, they must accept that a being defined by the negation of those roles cannot host change, exercise causation, or exist in any ontologically distinguishable sense. God collapses into ∅. This horn is doubly closed: the role-definition mapping establishes the collapse formally, and the theist's own descriptions of divine activity (acting in history, knowing what is currently the case, responding to prayer, creating at a moment) already instantiate the roles independently of the mapping. The classical project assigns to God a unique status (necessary existence) and the current Chapter 2 sequence establishes that this logical space is already occupied: the Modal Constraint Identified ([§2.5](<2.5 Triconditional Necessity.md>)), the Modal Identity ([§2.6.6](<2.6.6 Modal Identity.md>)), the Null State analysis ([§2.7](<2.7 Nothing to Consider.md>)), and the Necessity of Nature ([§2.8.5](<2.8.5 Necessity of Nature.md>)) together place necessary existence in the structure those roles constitute. Necessary existence, the classical God's defining modal status, belongs not to a being defined by the negation of the structural conditions but to Time, Space, and Substance as Nature. Nature is the necessarily existent ground. Divine simplicity, the claim that God is “all attributes at once without composition”, falls under this same horn, where [§6.2.1](<6.2.1 Simplicity.md>) has shown that simplicity strips what individuation requires.

*Horn two: Reject.* If the theist rejects the role definitions, they must provide an account of what Change requires that does not implicate Time, Space, and Substance. This requires showing that change is coherent without a before/after distinction, movement is coherent without relational extension, and interaction is coherent without a causal persistence medium. As established in [§1.4](<1.4 Three Conditions.md>), each denial is a direct contradiction of the logical content of the concepts being defined. The contemporary physical cosmology most relevant to Horn 2 presses the rejection of T-structure from the scientific side. Carroll's critique of Craig's cosmological arguments "Does the Universe Need God?", -(Sean M. Carroll, 2012); *The Big Picture*, -(Sean Carroll, 2016); -(Sean M. Carroll and Jennifer Chen, 2004) establishes that the Borde-Guth-Vilenkin (BGV) theorem, invoked regularly by Craig as establishing a cosmological beginning requiring a cause, establishes only that classically-described inflationary spacetime regions have geodesically incomplete past boundaries; it does not establish an absolute beginning of time in the classical sense. Hartle-Hawking no-boundary proposals (James B. Hartle and Stephen W. Hawking, 1983) and eternal-inflation models give the cosmological "beginning" a richer structure than simple T-asymmetry: the earliest boundary of the inflationary regime may be a Euclidean (imaginary-time) region in which ordinary temporal asymmetry dissolves rather than terminates at a singular boundary. Carroll's Bayesian framing further demands that any hypothesis about a cosmological cause be assessed against naturalistic alternatives (eternal inflation, quantum-gravitational no-boundary conditions, Carroll-Chen eternal inflation) on grounds of explanatory power and simplicity, rather than by application of the classical causal principle. The concern Horn 2 inherits from the scientific engagement is that the physical proposals still presuppose quantum-gravitational structure, Euclidean metric relations, and a physical substrate: they complicate the simple T-asymmetric beginning picture without removing the structural conditions their own descriptions require. Carroll's past-hypothesis, the stipulation of a low-entropy initial condition as the ground of the thermodynamic arrow (Albert, David Z., 2000); (Sean Carroll, 2010), sharpens rather than relieves the concern: it names the arrow-of-time explanandum by positing a structural T-asymmetry at the cosmological boundary, not by dissolving the before/after distinction the T-role defines; [§7.7](<7.7 Cosmic History.md>) develops the fuller treatment.

*Horn three: Redefine.* If the theist redefines God as a being that does instantiate Time, Space, and Substance, they have abandoned classical theism and with it aseity. A being that instantiates the structural conditions is embedded in structure and depends on it for its existence. The pantheist who responds that the deity is structure faces the relabeling closure of [§5.3.1](<5.3.1 Spinozist Pantheism.md>): structure is necessary, all-encompassing, and explanatorily basic, but it is not thereby personal, agential, intentional, or an object of worship. Re-labeling structure as God changes the word while conceding the substance. A stronger version of this horn proposes that the necessary structure is necessarily conscious: if consciousness consists in sufficiently integrated self-modeling (developed in [§7.8](<7.8 Life.md>)), perhaps any medium instantiating T, S, and Φ with sufficient complexity necessarily produces awareness. The response turns on substance-specificity ([§7.8](<7.8 Life.md>)): the character of experience is determined by the character of the organization that constitutes it. The necessary structure's “consciousness” would not be unified in a single subject, would not be directed toward objects of concern, would not be responsive to prayer, and would not constitute an “I” that stands in personal relationship to anything. On the most demanding version of the Third Horn, what is granted is Nature felt from inside at every point, not a being that knows, wills, loves, or commands. Process theism and open theism escape the ∅ charge against the classical God, but not the forfeiture of aseity: a God who exists in time and acts within the structure is a God who depends on the structure for that position. Swinburne's theistic personalism *The Coherence of Theism*, -(Richard Swinburne, 1977); *The Existence of God*, -(Richard Swinburne, 1979); -(Richard Swinburne, 2004); *The Christian God*, -(Richard Swinburne, 1994) is the most rigorous contemporary Horn 3 candidate: God is an everlasting person (omnipotent, omniscient, perfectly free) who exists in time, acts within the modal structure, and whose simplicity is the absence of physical constraints on the will rather than the absence of temporal or spatial location. Swinburne explicitly distances himself from divine atemporality and from the strong doctrine of divine simplicity that generates many of the chapter's inversions; on Swinburne's account, many of the chapter's pressures do not apply to his God at all. The concern for Swinburne's Horn 3 is comparative: the Swinburnian God is a personal agent whose existence is a brute but simple explanatory fact (Swinburne grants this), while the structural-necessity account posits T, S, and Φ as the necessary framework without a personal agent. The relative-simplicity question (is a necessarily existing structural frame simpler than a necessarily existing personal agent?) does not require a verdict on Swinburne's own probabilistic terms, and [§5.1.4](<5.1.4 Argument from Simplicity.md>) shows why those terms cannot reach it. Swinburne's simplicity is not itself a claim about prior probability but the a priori criterion that fixes the prior; and a prior is a measure over a space of possibilities, so where that space is not yet fixed, there is nothing for the criterion to fix. That space is not contingent furniture: the Modal Identity ([§2.6.6](<2.6.6 Modal Identity.md>)) and the Necessity of Nature ([§2.8.5](<2.8.5 Necessity of Nature.md>)) establish that the space of genuine possibilities is fixed necessarily and that it is Time, Space, and Substance. A Bayesian comparison therefore presupposes that structure as the condition under which it assigns any prior at all, and so cannot be the instrument that ranks the modal structure against a proposed alternative to it: the comparison runs between inhabitants of Nature, never between Nature and a rival ground, because the measure it would use is defined only once Nature is in place. The single construction that would make Swinburne's God such a rival ground (a personal agent grounding the structure while standing in no real relation to it) returns it to Horn 1, where [§4.2.1](<4.2.1 The Changeless Ground.md>) and [§6.8.2](<6.8.2 Relatability.md>) establish that a ground bearing no real relation to what it grounds preserves the name and surrenders the structure, reducing to ∅. The comparative question therefore closes under the trilemma rather than alongside it. What chapters 7–9 carry forward is not a probabilistic contest with theistic personalism but the positive account of Nature as the one necessary modal structure.

*The conjunction-level line.* The Trilemma Closure reaches the result without assuming anything about God's modal standing. A faster line reaches the same verdict directly, at the cost of one added assumption. The classical commitments are three: simplicity, *actus purus* (pure actuality: a being with no unrealized potential, nothing in it waiting to be made actual), and immutability. They converge on a single doctrinal claim: God has no alternative way to be. By the tradition's own description, God could not have been otherwise.

> [!argument]
> **The no-way-possible argument** · *The Conjunction-Level Line*
>
> 1. God has no alternative way to be: by the tradition's own commitment to simplicity, *actus purus*, and immutability, God could not have been otherwise.
>
> 1. To be possible (as a modal subject) is to be one way *rather than* another. This is the semantic content of *possible* when the predicate is applied substantively to a being whose modal status the predicate is supposed to track ([§3.2.5](<3. Convergence.md>) develops the decomposition via the Modal-Vocabulary Line's Way–Possibility Convertibility; the *rather-than* structure is constitutive of substantive modal predication). The one escape at this step is analogical predication (that *possible* is said of God not univocally but by analogy, so the *rather-than* structure need not bind) and it is closed on its own terms at [§6.2.1](<6.2.1 Simplicity.md>), where analogical predication is shown to require a real divine correlate that either collapses into synonymy or readmits the very distinction it was invoked to avoid.
>
> 1. ∴ The classical theist's God is not possible. *(1, 2)*
>
> 1. What is not possible is impossible.
>
> 1. ∴ The classical theist's God is impossible.

The argument does not add a new premise. It makes explicit what the role-definition mapping of §[§6.1](<6.1 Greatness.md>)–6.9.2 establishes: the classical commitments converge on the doctrinal claim that God has no alternative way to be; the predicate *is possible*, when applied substantively to a modal subject, just *is* the alternative structure; and these two together fix the modal verdict. The descent runs cleanly: *no alternative → no possibility → not possible → impossible*. This is the conjunction-level line: the quickest road, and the one that runs on the substantive-modal-subject assumption the next paragraph isolates. Its advantage over the Trilemma Closure is speed; its cost is that the assumption can be refused, which is why the Trilemma Closure, not the argument, is the theorem's proof of record.

One presupposition the argument runs on deserves explicit acknowledgment: it assumes God is a modal subject, a being to whom the substantive predicate *is possible* applies in the sense that tracks a being's modal status across worlds. The sophisticated classical theist may refuse this assumption, holding instead that God grounds the modal structure rather than fitting within it (Leftow, Brian, 2012); (Thomas V. Morris and Christopher Menzel, 1986); (Pruss, A. R., 2011). On that refusal, *is possible* does not apply to God substantively, and the argument does not arise, but the Trilemma Closure, which makes no such assumption, still does. The refusal pays its own costs: substantive modal predication of God collapses (*necessarily exists* loses its modal content), and the grounding act itself requires the structural roles it was supposed to make possible. Those costs are tracked at [§6.3.1](<6.3.1 Necessity.md>), Q1 (modal candidacy of the subject) and [§6.3.1](<6.3.1 Necessity.md>), Q6 / [§6.7.2](<6.7.2 Causality.md>), Q7 (the grounding act).

*The necessity rescue.* A second classical reply concedes the argument's possibility verdict but holds that God's *necessity* puts God beyond it: a necessary being, the Thomist says, does not stand under the possibility predicate the way contingent beings do. The reply runs against the *Necessity entails Possibility* result derived at [§2.1.4](<2.1.4 Modal Stability.md>): □P → ◇P, falling out of the T-axiom composed with the *actuality implies possibility* result of [§1.2](<1.2 Modal Status.md>). Contraposed: ¬◇P → ¬□P — what is not possible is not necessary. The argument establishes that the classical God is not possible. The result then delivers that the classical God is not necessary either: the necessity ascription does not survive the impossibility verdict but falls with it. The Thomist who reaches for necessity to exempt God from the verdict reaches for a predicate the same verdict has already foreclosed.

*The cumulative case.* God is defined as the conjunction of its classical attributes, and every attribute in that conjunction has been shown to reduce to a structural role already instantiated by Time, Space, and Substance. The reductions are not all independent: most run through one of two master results, the simplicity/differentiation dilemma ([§6.2.1](<6.2.1 Simplicity.md>)) and the directed-crossing result ([§5.3.3](<5.3.3 Process Theology.md>)), applied to one attribute's vocabulary after another. The cumulative force is therefore concentrated rather than additive, strongest where those two results are strongest, and a successful challenge to either would propagate across the attributes that depend on it. This concentration is a feature of the cumulative case, not a vulnerability of the result: the theorem's proof of record is the Trilemma Closure, which assumes nothing about the attribute-by-attribute reductions and stands whatever becomes of them. The cumulative case corroborates the verdict; it does not carry it. What remains after the relocation is not a being with diminished attributes. It is Time, Space, and Substance themselves, now carrying the functional work the attributes were supposed to perform, with nothing left over that could distinguish God from the structure it was meant to transcend. The standard incompossibility-of-maxima objection, that the perfections, even granted individually, cannot coherently obtain in a single being (Jordan Howard Sobel, 2004); (Martin, Michael, 1990); (Everitt, Nicholas, 2004), surfaces here as the cumulative form of the concern the chapter has been pressing: each attribute has already been pressured at its individual point, and the question the cumulative case raises is whether the failures, taken jointly, leave any coherent residue for the perfect-being-theology engine to have produced. Theorem 8's formal result carries a direct implication for the modal ontological argument. Plantinga's -(Plantinga, A., 1974) S5 argument advances from ◇(maximal greatness is instantiated) to □(God exists) via S5: if it is possible that maximal greatness is instantiated, and maximal greatness entails necessary existence, then by S5 maximal greatness is instantiated in every possible world. [§6.2.4](<6.2.4 Perfection.md>) Q2 and Q4 establish that the classical great-making bundle does not cohere as a possible specification of a single being under the structural constraints the chapter has developed; Theorem 8 states the result formally: the conjunction of classical attributes has no possible world. If the bundle is not possibly co-instantiated, Plantinga's first premise (*it is possible that maximal greatness is instantiated*) is blocked at the point of entry, and the S5 inference does not run. Plantinga's de re reading presses whether Theorem 8's impossibility is of the being itself or of the description applied: on the de re reading, the question is whether the very entity the argument quantifies over is one that could exist; on the de dicto reading, the question is whether the description *maximally great being* is possibly satisfied. The chapter's structural analysis applies at both levels (the structural conditions T, S, and Φ bear on any entity that would have to satisfy the description, not merely on how the description is worded) and the de re/de dicto distinction does not provide an escape from Theorem 8.

*Mysterious ways.* The tradition's most common fallback under pressure (*God's reasons exceed our understanding*) is not a fourth horn but a refusal to occupy any. It is invoked asymmetrically: deployed to rescue coherence under objection, never allowed to unsettle attributions made in confidence (*God is love, is just, is creator*). The closure of §[§6.1](<6.1 Greatness.md>)–6.9.2 addresses what the tradition has stated, not what it knows but refuses to state. Each attribute was given determinate content every time it was preached, prayed, or predicated. The retreat either keeps that content (in which case the modal argument applies) or withdraws it, in which case the attribute no longer means what the tradition has been using it to mean. [§6.8.3](<6.8.3 Describability.md>) closes the apophatic form of this move; the present paragraph closes its generic form. The appeal to mystery does not open a third option between having content and lacking it. It defers to a domain the argument has not entered (the inner life of divine being) rather than addressing the structural question the argument has pressed, which concerns not what God is but whether the predicates applied to God retain the content required for them to function as predicates at all.

*Refusing the trilemma.* The deepest form of the move is to refuse the trilemma itself: God neither falls inside the disjunction nor stands outside it; the predicates apply at a level the disjunction does not reach. The refusal is not a fourth horn. It is either a real refusal (a structured act of declining to predicate, performed in this discourse at this moment, actualizing silence over assertion) in which case the refusal instantiates the contrast between what is and is not actualized, and the modal pressure that runs through agency runs through it; or it is not a real refusal, in which case nothing has been said and the doctrine has dissolved into ∅ from the side of speech rather than from the side of being. Modal pressure is not pressure on what to say. It is pressure on what counts as having said anything at all. There is no position from which the predicates can be neither affirmed nor denied without that position itself being one of the things the predicates were supposed to characterize. The refusal to occupy a horn is the occupation of one. The performative-denial argument of [§3.3](<3.3 Triconditional Necessity Negative Account.md>) runs the same closure from the side of denial; the present paragraph runs it from the side of withholding.

A single image collects the inversions. Consider God as an Author: the being whose word calls the world into existence. The target here is the classical Author predicate, not religious devotion or the people who speak from within it. To begin writing, the Author must transition from not-writing to writing: that is Time. To set the first word on a page, the Author must direct the act toward a surface at a location: that is Space. To hold the pen, the Author must stand in causal-persistence contact with a material instrument: that is Substance. To conceive the plot, the Author must distinguish what comes first from what comes next. To sign the finished work, the Author must persist as the same agent from the first stroke to the last. To reach an audience, the Author must be relationally distinct from the readers. Each inversion names a different structural requirement authorship carries. The predicate cannot begin, draw, hold, conceive, sign, or reach without the very conditions the classical definition denies. The tradition calls God the Author of the world. The modal account reads the same vocabulary differently: God is defined by the absence of everything authorship (and therefore creation) consists in.

> [!theorem]
> **Supernatural Preclusion** · **T8** · *Theorem 8*
>
> The conjunction of classical attributes (atemporality, aspatial existence, immateriality, divine simplicity, aseity) faces a trilemma of specification. If it accepts the chapter's role analysis while withdrawing every differentiating feature and determinate relation, it incurs the ∅-like failure of specification the discernibility principle identifies. If it rejects the role analysis, it owes a coherent alternative account of change, distinction, and grounding. If it relocates the deity within temporal, relational, and active structure, it revises the classical aseity claim. The theorem records this burden and the structural cost of each response; a separate essence-prior posit remains answerable only when it supplies a determinate grounding account. ([§6.1](<6.1 Greatness.md>), [§2.8.5](<2.8.5 Necessity of Nature.md>))

> *Proof (Trilemma Closure).* Notation: H1 = Accept the role definitions; H2 = Reject the role definitions; H3 = Redefine God to instantiate them — the three horns developed above.
>
> 1. H1 ∨ H2 ∨ H3 — the chapter's three principal responses: accept the role analysis, contest it, or revise the deity to realize the roles.
>
> 1. H1 → a God stripped of every differentiating feature and determinate relation incurs the ∅-like specification problem (role mapping, §[§6.1](<6.1 Greatness.md>)–6.9.2; discernibility premise, [§5.2.1](<5.2.1 Divine Simplicity.md>), [§2.7](<2.7 Nothing to Consider.md>)).
>
> 1. H2 → the theorist owes a coherent rival analysis of change, distinction, and grounding without the relevant roles ([§1.4](<1.4 Three Conditions.md>); Horn 2).
>
> 1. H3 → the deity is configured within Nature and incurs a revised aseity burden ([§6.1](<6.1 Greatness.md>)).
>
> ∴ The classical package is not preserved without either an ∅-like specification problem, a rival structural theory, or a revision of classical aseity. ∎

In ordinary terms: a God outside the structural conditions cannot act, relate, or be distinctly specified; a God inside them may be a real being, but is no longer the independent ground classical theism requires.

What Nature is, the classical family of doctrines (Christian-Scholastic, Jewish, Islamic, and the formally parallel developments beyond them) has in each of its formulations been reaching for and naming as a being beyond Nature. Oppy's total-theory framework *Arguing about Gods*, -(Oppy, Graham, 2006); *Naturalism and Religion*, -(Graham Oppy, 2018) places the sharpest demand on the closing result: the relevant standard of assessment for Theorem 8 is not whether classical theism has a possible world taken in isolation, but whether a total theory that includes classical theism is simpler, more comprehensive, and more explanatorily powerful than the best naturalistic rival. Initial-state naturalism (on which the universe's initial conditions are the unexplained brute structural fact) is the relevant rival: both the structural-necessity account and classical theism posit something necessarily existing; the question is which total theory yields the simpler, more economical account of why anything exists and why it has the structure it has. Oppy's naming-vs-thing challenge surfaces at the chapter's closing sentence: if the classical tradition was reaching for what the chapter calls Nature, the chapter's Nature fills God's functional roles — necessary existence, explanatory ground, the condition of any possible world. What principled distinction separates calling this Nature from calling it God, other than the label? The chapter's reply is structural rather than nominal: Nature is not personal, not agential, not intentional, and not a subject in the second-personal sense the believer's confession requires; the classical attributes presuppose structural conditions that any subject bearing them would have to instantiate, and the chapter's analysis of those conditions is a disambiguation of what the conditions name rather than a relabeling of the same referent. One asymmetry the reply can make precise here, rather than deferring it whole. The PSR-symmetry objection (that Nature's brute necessity is no less in need of grounding than God's) treats the two necessities as the same kind. They are not. Nature's necessity is *modal-structure necessity*: the necessity of the modal structure itself, which [§6.2.2](<6.2.2 Unity.md>) shows can have no external ground, since a second modal structure that could ground it would require a more comprehensive modal structure the two were alternatives within, and so just *is* the one modal structure. A God's necessity, by contrast, would have to be *inhabitant-necessity* (the necessity of a being within the modal structure) and [§6.3.1](<6.3.1 Necessity.md>) (Q1, Q8) establishes that the modal structure's modal status does not transfer to any inhabitant of it. Modal-structure necessity is the only necessity that needs no further ground, precisely because it is not the necessity of a thing but the structure within which thing-necessity is reckoned; inhabitant-necessity always presupposes the modal structure. That is the principled distinction Oppy's naming-challenge demands, and it is argued for, not merely posited. [§6.2.2](<6.2.2 Unity.md>) and [§6.3.1](<6.3.1 Necessity.md>) carry it, on a premise that is itself established rather than assumed: that any ground of the modal structure would itself have to be a modal structure. Theistic activism resists this, locating the modal facts in a divine intellect or will; its denial is closed on its own terms: at [§4.1.10](<4.1.10 The Source of Possibility.md>), where Modal Exclusivity shows by elimination on a candidate's own modal status that possibility has no source (an impossible ground has no relata, a contingent one presupposes the field, a necessary one is a feature of the field already in place), and at [§5.1.8](<5.1.8 Modal-Grounding Argument.md>), where the conceptualist and voluntarist versions of the divine-grounding move are shown to collapse under their own demands or to converge on the structural account. The difference between Nature and a god is not the label but the difference between being the modal structure and being something the modal structure would have to host. Oppy's challenge is sharpened rather than dissolved by this reply (it remains the right challenge to press against any pantheism-adjacent inversion) and the fuller positive account of why the structural analysis is not merely nominal is what chapters 7–9 carry.

To exist is to take place, and God is defined as taking no place at all. *Toward, from, between, above, there*: each direction the doctrine forecloses is a direction Nature cannot do without. There is no exit, because the structure the tradition sought to stand outside is the Nature it was already within.


---

← [6.9.2 Righteousness](<6.9.2 Righteousness.md>) | [7. Nature Alone](<7. Nature Alone.md>) →
