The Grammar of Relation in Theology

§1. Why Relations Matter in Theology

Theology speaks incessantly of relations. God creates the world, Christ is present in the believer, the Spirit proceeds, faith justifies, the Word reveals, the creature depends upon God. None of these claims is primarily a claim about things taken in isolation. They are claims about how realities stand to one another. Yet theology has often treated such relations as if they were rhetorically obvious or metaphysically harmless, requiring no explicit clarification.

This has proven costly, for much contemporary theological disagreement does not arise from conflicting doctrines so much as from unexamined relational assumptions. One theologian assumes that causation must be symmetric, another that participation implies identity, a third that dependence must be transitive, a fourth that identity licenses substitution in all contexts. Arguments then proceed as if these assumptions were self-evident, when in fact they differ at the level of grammatical form rather than doctrinal content. Lamentably, when that happens, disagreement becomes opaque. Theology begins to speak past itself.

The purpose of this essay is not to advance a new doctrine, nor to resolve disputed loci. It is more modest and more foundational. Its aim is to make explicit the relational grammar that theology already presupposes whenever it speaks clearly. Relations here are not metaphors, nor heuristic conveniences. They are formal structures that govern intelligibility itself. To ignore them is not to remain neutral; it is to operate blindly.

This concern is not alien to the theological tradition. Luther’s insistence upon a nova lingua was never a call for linguistic novelty as such. It was a recognition that theological language obeys a grammar determined by its object. To speak rightly of God requires more than pious intention; it requires disciplined attention to the forms of predication, causation, and dependence appropriate to divine–creature relations.

What follows, then, is an exercise in grammatical clarification. We will distinguish kinds of relations, note their formal properties, and indicate—without yet arguing doctrinal conclusions—why theology cannot dispense with these distinctions. The aim is not formalism for its own sake, but clarity: clarity about what theology is already doing when it speaks meaningfully at all.

§2. Relations as Grammar, Not Theory

When theology speaks of relations, it is tempting to hear these as theories—claims added to an otherwise complete ontology. One might think, for example, that to say the believer is “related” to Christ is to introduce an explanatory hypothesis alongside others: causal, psychological, symbolic, or social. Under that assumption, relations appear optional or revisable, depending on one’s broader metaphysical commitments. But this assumption is mistaken.

Relations function in theology not primarily as theories but as grammar. They determine how claims may be made before determining which claims are true. To confuse grammar with theory is to treat the conditions of intelligibility as if they were empirical hypotheses. But grammar is not proposed; it is presupposed. It governs what counts as a coherent assertion in the first place.

This is already familiar in ordinary language. The difference between “x causes y,” “x resembles y,” and “x is identical with y” is not a difference in empirical content alone. It is a difference in grammatical form. Each licenses different inferences and forbids others. To mistake one for another is not to adopt an alternative theory; it is to speak incoherently.

The same is true—a fortiori—in theology, because when theology asserts that God creates the world, it is not free to treat creation as symmetric, reversible, or reflexive. When it speaks of participation, it must avoid identity without reducing participation to metaphor. When it speaks of revelation, it must distinguish dependence from grounding, mediation from causation, presence from locality. These distinctions are not optional refinements. They are grammatical constraints imposed by the subject matter itself.

Luther’s insistence that theology has its own lingua is best understood in precisely this way. The nova lingua is not a poetic overlay on ordinary speech, nor a pious distortion of philosophical language. It is the recognition that the object of theology—the living God—determines the grammar under which speech about God is possible. Where that grammar is ignored, theological language does not become freer; it becomes confused.

For this reason, making relational grammar explicit is not an act of formal domination over theology. It is an act of obedience to theology’s own internal demands. Formalization, when it comes, does not replace judgment or confession. It disciplines them. It makes visible the distinctions theology already relies upon whenever it avoids triviality or contradiction.

In the next section, we move from description to formal grammar. The aim is not to impose alien machinery upon theology, but to state precisely the relational forms theology cannot avoid using if it is to speak at all.

§3. The Formal Grammar of Relation

We now state explicitly the relational grammar presupposed in the preceding discussion. The purpose of formalization here is not reduction but clarification. What follows does not introduce new theological claims; it renders explicit the logical forms already operative whenever theology speaks coherently of causation, presence, participation, revelation, or justification.

Let $\mathrm{<br>}{\mathrm{D1\; \&\; D2\; be\; domains\; and\; let <br>}}_{}$$R\subseteq {\mathrm{<span\; style="text-transform:\; math-auto;">D1\; x\; D2\; be\; a\; binary\; relation.</span>}}_{}$

3.1. Reflexivity and Its Variants

A relation $R \subseteq D \times D$ is:

• Reflexive iff (∀x ∈ D)Rxx

• Non-reflexive iff ~(∀x ∈ D)Rxx

• Irreflexive iff (∀x ∈ D )~Rxx

Grammatical note.
Theological causation is never reflexive; divine aseity is not self-causation. Failure to distinguish non-reflexivity from irreflexivity routinely generates pseudo-problems.

3.2. Symmetry, Asymmetry, and Antisymmetry

A relation $R \subseteq D \times D$ is:

• Symmetric iff (∀x ∈ D)(∀y ∈ D) (Rxy → Ryx)

• Non-symmetric iff ~(∀x ∈ D)(∀y ∈ D)(Rxy → Ryx)

• Asymmetric iff (∀x ∈ D)(∀y ∈ D)(Rxy → ~Ryx)

• Antisymmetric iff (∀x ∈ D)(∀y ∈ D)[ (Rxy ∧ Ryx) → x = y]

Grammatical note.
Antisymmetry is the formal safeguard against ontological collapse. Participation without identity is unintelligible without it.

3.3. Transitivity and Its Limits

A relation $R \subseteq D \times D$ is:

• Transitive iff (∀x ∈ D)(∀y ∈ D)(∀z ∈ D)[(Rxy ∧ Ryz) → Rxz]

• Non-transitive iff ~(∀x ∈ D)(∀y ∈ D)(∀z ∈ D)[(Rxy ∧ Ryz) → Rxz]

• Intransitive iff (∀x ∈ D)(∀y ∈ D)(∀z ∈ D)[(Rxy ∧ Ryz) → ~Rxz]

Grammatical note.
Illicit theological arguments often assume transitivity where only mediated dependence is licensed.

3.4. Connectivity (Connexity)

A relation $R \subseteq D \times D$ is connected iff (∀x ∈ D)(∀y ∈ D)[x ≠ y ∧ (Rxy ∨ Ryx]

Connectivity distinguishes total from partial orders and becomes decisive in teleological and eschatological contexts.

3.5. Composite Relational Structures

The following complexes are presupposed:

• Equivalence relation: reflexive, symmetric, transitive

• Strict partial order: irreflexive, transitive

• Partial order (poset): reflexive, antisymmetric, transitive

• Total (linear) order: partial order plus connectivity

• Tolerance relation: reflexive, symmetric, non-transitive

These structures are grammatical resources, not metaphysical theses.

3.6. Typed Relations

Relations are not assumed to range over a single homogeneous domain.

Formally: R : D1 × D2​

Typed relations govern divine–creature discourse, Logos–world relations, Spirit–language relations, and cause–effect structures. Ill-typed relations are excluded prior to argument.

3.7. Dependence and Grounding

Two distinct relational notions are presupposed:

• Dependence: a structural priority relation

• Grounding: a constitutive relation determining what something is

Grounding is not reducible to efficient causation, and dependence does not entail grounding.

3.8. Hyperintensional Non-Substitutivity

Relational contexts are not assumed to be extensional.

Even where x = y it does not follow that Rxz ↔ Ryz

Grammatical note. Theological predication, Christological communication, and participatory ontology all require such contexts. Extensional substitution here produces category mistakes, not clarity.

This formal grammar does not replace theological judgment. It makes judgment possible. In the next section, we will indicate why theology cannot be extensional and what this grammar clarifies—without yet drawing doctrinal conclusions.

§4. Typed Relations, Dependence, and Grounding

The formal grammar introduced in the previous section would remain abstract were it not applied to a central theological problem: how realities of fundamentally different kinds may be related without confusion or collapse. Theology cannot avoid this problem, because its subject matter is constituted by asymmetric relations between non-homogeneous domains—God and creature, Word and world, Spirit and language.

4.1. Why Relations Must Be Typed

In much modern discourse, relations are tacitly assumed to range over a single undifferentiated domain. This assumption works tolerably well in restricted contexts—social relations, numerical orderings, empirical causation—but it becomes destructive when imported into theology.

Theological relations are almost always typed. They relate terms drawn from different ontological orders. Creation does not relate one creature to another; it relates the Creator to what is not God. Revelation does not relate one proposition to another; it relates the living Word to finite language. Justification does not relate two moral agents symmetrically; it relates God’s act to the sinner.

Formally, such relations take the shape: R : D1 × D2 where D1 ≠ D2.

Once this is acknowledged, entire classes of pseudo-questions disappear. One need not argue that the creature cannot ground God, or that faith cannot justify Christ. These proposals are not false; they are ill-typed. They violate the grammar of theological discourse before they reach the level of doctrine.

4.2. Dependence as Structural Priority

Within typed relations, theology frequently speaks of dependence. Creatures depend upon God; faith depends upon the Word; theology depends upon revelation. Dependence names a relation of priority or reliance, but it does not yet specify what confers being or intelligibility.

Formally, dependence is a structural ordering relation. It may be asymmetric and often transitive, but it remains compatible with mediation, contingency, and plurality of levels. To say that x depends on y is not yet to say how y makes x what it is.

Confusion arises when dependence is either inflated into efficient causation or reduced to epistemic access. In theology, dependence frequently names an order of reception rather than a mechanism of production.

4.3. Grounding as Constitutive Relation

Grounding is stronger. To say that y grounds x is to say that y is constitutive of x—that x is what it is in virtue of y. Grounding answers a different question than dependence. It concerns not priority in sequence or explanation, but intelligibility in being.

This distinction is indispensable for theology. Faith may depend upon preaching in time, but it is grounded in the Spirit’s act. Theological language may depend upon historical usage, but it is grounded—if it is theology at all—in divine self-giving. Justification may depend upon proclamation, but it is grounded in Christ’s righteousness.

Failure to distinguish dependence from grounding produces either voluntarism (everything depends on divine choice alone) or reductionism (everything reduces to finite processes). Theology requires neither.

4.4. Grounding Without Mechanism

It is important to note what grounding is not. It is not a causal mechanism, nor a hidden process operating behind appearances. Grounding does not compete with finite causes, nor does it displace them. It names a relation of ontological constitution, not temporal production.

This point bears directly on theological realism. To say that divine action grounds finite reality is not to introduce an extra item into the causal inventory of the world. It is to say that the world is intelligible only because it stands in a constitutive relation to God.

Here again, grammar precedes doctrine. Without a notion of grounding distinct from dependence and causation, theology oscillates between collapse into metaphysics or retreat into metaphor.

4.5. Why These Distinctions Matter

Typed relations, dependence, and grounding together secure a space in which theology can speak ontologically without confusion. They allow theology to affirm real relations between God and the world while preserving asymmetry, avoiding identity, and resisting reduction.

They also prepare the way for a final clarification: why theological discourse cannot be extensional, and why substitution—even under identity—fails in precisely the contexts theology inhabits. That clarification is the task of the next section.

§5. Why Theology Is Not Extensional

Much modern philosophy of language proceeds under an extensional ideal: if two terms refer to the same object, they may be substituted salva veritate in all contexts. Within restricted domains—arithmetical identity, empirical description, purely extensional predicates—this assumption is often harmless. In theology, it is not merely inadequate; it is destructive.

The reason is now clear. Theological discourse is governed by relations that are typed, asymmetric, often grounding rather than merely dependent, and irreducible to causal or descriptive mechanisms. Such relations generate hyperintensional contexts, in which identity does not license unrestricted substitution.

Formally, even where x = y, it does not follow that Rxz ↔ Ryz. This is not a technical anomaly. It is the normal condition of theological predication.

5.1. Predication Under Relation

Theology rarely predicates properties of isolated subjects. It predicates under relations: Christ as incarnate, God as creator, the believer as justified, the Word as proclaimed. These relational contexts are constitutive of meaning. Remove them, and the predicate either collapses into triviality or shifts into a different register altogether.

For this reason, theological identity claims do not function like numerical identities. To say that Christ is God is not to say that every predicate applying to “God” may be substituted unmodified into every predicate applying to “Christ.” The communicatio idiomatum itself presupposes controlled non-substitutivity. Without it, Christology oscillates between Nestorian separation and monophysite collapse.

5.2. Participation Without Collapse

The same is true of participatory language. When theology says that the believer participates in divine righteousness, it does not assert identity of essence. Antisymmetry and non-substitutivity together make this intelligible. The believer is really related to divine righteousness without becoming identical with God. Extensional substitution would force precisely the conclusion theology must deny.

Participation, therefore, is not a metaphor masking identity, nor a resemblance disguising distance. It is a real relation whose grammar forbids collapse.

5.3. Grounding and Theological Reference

Non-extensionality is equally decisive for theological reference. If divine grounding is constitutive of finite being and meaning, then reference to God is not secured by descriptive equivalence alone. Theological language functions in contexts where what grounds reference matters, not merely what satisfies a description.

This is why theological terms cannot be replaced indiscriminately by functional or phenomenological equivalents without remainder. Even if two descriptions converge extensionally, they may diverge grammatically. Theology must attend to that divergence or abandon its claim to speak of God rather than merely about human experience.

5.4. The Cost of Extensionalism

Where extensional assumptions are imposed upon theology, the result is not increased rigor but systematic distortion. Christology becomes incoherent, sacramental presence collapses into symbolism, justification is reduced to moral status, and revelation is re-described as religious awareness. Each move appears modest in isolation; together they evacuate theology of its subject matter.

These are not errors of inference. They are errors of grammar.

5.5. Grammar as Theological Discipline

To say that theology is not extensional is not to deny clarity or truth. It is to insist that clarity requires discipline appropriate to the object spoken of. Grammar here functions as a form of theological restraint. It prevents theology from saying more—or less—than it is entitled to say.

The point may be stated simply. Theology does not become confused because it lacks information. It becomes confused when it forgets the relational grammar that makes its speech possible at all.

In the final section, we will indicate what this grammar clarifies, and why making it explicit does not constrain theology but frees it for disciplined disagreement and genuine advance.

§6. What This Clarifies—and Why It Matters

The purpose of this essay has been neither to construct a theological system nor to adjudicate disputed doctrines. Its aim has been more elementary and more enduring: to make explicit the grammar of relation that theology already presupposes whenever it speaks coherently of God, the world, and their communion.

By distinguishing kinds of relations—reflexive and irreflexive, symmetric and asymmetric, transitive and intransitive—and by attending to typed relations, dependence, grounding, and non-extensional contexts, we have not added content to theology. We have clarified the conditions under which theological content can be meaningfully articulated at all. Where these distinctions are ignored, theology does not become simpler; it becomes unstable.

Several persistent confusions are thereby brought into focus. Apparent disputes about causation often turn out to be disagreements about transitivity. Debates over participation frequently mask unresolved tensions between antisymmetry and identity. Conflicts over revelation and reference regularly presuppose incompatible assumptions about extensional substitution. In each case, what appears to be a doctrinal impasse is often a grammatical failure.

Making this grammar explicit serves a constructive purpose. It allows theology to affirm real divine–creature relations without collapse, to speak ontologically without mechanizing divine action, and to maintain the integrity of theological language without retreating into metaphor or subjectivism. It also permits disagreement to become precise. When the grammar is shared, disagreement can be located where it belongs—at the level of ontological commitment or theological judgment—rather than being diffused into ambiguity.

This clarification also situates formalization rightly within theology. Formal grammar does not govern theology from without; it serves theology from within. It renders explicit the distinctions theology already enacts in its best moments. To formalize is not to dominate but to attend—to the object that commands theological speech and to the discipline required to speak truthfully of it.

Finally, this essay marks a boundary. It explains why certain matters have been treated only implicitly elsewhere and why fuller formal exposition belongs to particular genres of theological work. Not every text must carry its grammar on its sleeve. But theology cannot dispense with grammar altogether without forfeiting intelligibility.

If this essay succeeds, it will have done something modest but necessary. It will have shown that before theology can argue, it must first know how it is speaking—and that such knowledge is not ancillary to theology, but part of its fidelity.

On Intelligibility, Determinability, and the Logos Who Makes Meaning Possible

For many years I have been puzzled by a question that refuses to dissolve: how are transcendental arguments possible at all? How can one speak meaningfully about the conditions for the possibility of experience, knowledge, or formalization without already presupposing what one claims to ground?

Logic and mathematics have sharpened this question rather than resolved it. Formal systems are extraordinarily powerful. They model relations, generate derivations, and articulate vast domains of structure. Yet the more rigorous they become, the more clearly they reveal something they cannot contain: the space in which they are intelligible as systems in the first place.

Gödel made this unavoidable. A sufficiently expressive system can represent its own syntax, yet it cannot secure from within the distinction between truth and provability. Even when meta statements are themselves formalized, the recognition that the formalization is adequate occurs at a higher level still. The meta recedes as it is captured. What is gained in rigor is accompanied by a renewed excess.

This excess is not merely epistemic. It is not simply a limitation of human cognition or a gap in symbolic technique. It belongs to intelligibility itself. Formal systems presuppose a horizon in which interpretation, relevance, adequacy, and meaning are possible at all. That horizon is not a theorem. It is the condition under which theorems can appear as meaningful.

Here a structural parallel becomes visible. The transcendental I cannot be thought as an object without ceasing to be transcendental. An I that is thought is already a higher order self, something represented rather than that by virtue of which representation occurs. The condition of objectivity cannot itself be an object in the same register without contradiction. This is not a contingent limitation. It is structural.

Something analogous occurs with intelligibility itself. Once a teleological space of meaning is determined, named, or even ontologically affirmed, that determination presupposes another horizon within which it is intelligible as a determination. The sine qua non of the determined as determined is not a further determination, but an indeterminate field that allows for determinability. The indeterminate does not issue in form. It makes form possible.

This is the insight Kant reached most clearly in the Third Critique. Determining judgment subsumes particulars under given rules. Reflecting judgment seeks the rule under which particulars may be unified without possessing that rule in advance. Reflecting judgment operates within a teleological space, oriented toward coherence and purposiveness without algorithmic closure. This space is not subjective whim. It is the condition under which object languages can be coordinated at all.

Seen in this light, intelligibility is teleological not because it aims at a humanly imposed end, but because it orients formal structures toward meaning without compelling their form. Formal systems are not self originating. They are drawn into being by the possibility of meaning that precedes them. This possibility is real, but it is not itself formal. It orders without determining. It attracts without necessity.

This is why attempts to algorithmize theory change inevitably fail. To formalize the rules of revision presupposes prior judgments of relevance, adequacy, and success that exceed the system being revised. The ladder by which a system ascends cannot be retained within the system without contradiction. The indeterminate that allows for determinability cannot be collapsed into determination without loss.

Here the question of Logos re emerges with new clarity. Logos is not first a word spoken, nor an idea grasped, nor a system constructed. Logos names that by virtue of which meaning is possible at all. It is the order that permits articulation without exhausting itself in articulation. It is the ground that calls without coercing, that grants intelligibility without dictating form.

“In the beginning was the Logos” is therefore not a temporal claim but an ontological one. In the beginning was that by virtue of which anything could be said, meant, or understood. Formal systems, scientific theories, languages, and even our most advanced machines live within this space. They do not create it. They respond to it.

To remember this is not to retreat from rigor but to fulfill it. Logic itself teaches that intelligibility cannot be fully objectified without remainder. That remainder is not a defect. It is the sign that meaning is grounded more deeply than any system can contain.

On Christmas, it is fitting to recall that the Logos who grounds intelligibility did not abolish finitude, form, or history, but entered them. The Word became flesh. Meaning did not collapse into mechanism, nor did transcendence remain aloof. The determinate was upheld by the indeterminate, and the finite was made capable of bearing what it could not generate on its own.

This is not sentiment. It is metaphysics. And it is, perhaps, the deepest reason theology and philosophy still find themselves speaking about the same thing—if only we are patient enough to listen.

Disputatio XXIIIa: De Sermone Meta-Theoretico et Intelligibilitate Formali

 On Meta-Theoretical Discourse and Formal Intelligibility

Quaeritur

Utrum intelligibilitas formalis systematum logicorum et mathematicorum praesupponat discursum metalinguisticum irreducibilem ad linguam obiectivam; et utrum hic excessus non solum epistemicus sed ontologicus sit, ita ut ipsa possibilitas significationis in rebus fundetur; et utrum hic fundus intelligibilitatis recte intelligatur ut spatium teleologicum, quod systemata formalia non efficiunt sed quod ipsa attrahit et constituit.

Whether the formal intelligibility of logical and mathematical systems presupposes a metalinguistic discourse irreducible to object language; and whether this excess is not merely epistemic but ontological, such that the very possibility of signification is grounded in things themselves; and whether this ground of intelligibility is rightly understood as a teleological space which formal systems do not produce but which draws them forth and constitutes them.

Thesis

Formal systems do not generate intelligibility. They presuppose it. Every object language capable of truth conditions relies upon a meta-discourse that cannot be fully internalized without loss of the very properties that render the system intelligible. This excess is not merely epistemic but ontological. The possibility of meaning precedes formalization and belongs to the structure of reality itself.

This irreducible space of intelligibility may be described as teleological: not as an imposed purpose or subjective projection, but as the permanent possibility of meaningful determination that draws formal systems into being and coordinates their interpretation. Metalanguage thus testifies to an order of meaning that no formal system can exhaust, yet without which no formal system can be what it is.

Locus classicus

Gödel, Über formal unentscheidbare Sätze (1931)
“Es gibt innerhalb eines jeden hinreichend mächtigen formalen Systems wahre Sätze, die innerhalb dieses Systems nicht beweisbar sind.”

“There are, within every sufficiently powerful formal system, true propositions that cannot be proven within that system.”

Gödel’s result is not merely technical. It reveals that truth outruns formal derivability and that the conditions for recognizing truth are not fully capturable by the system whose truths are in question.

Peirce, Collected Papers 5.121
“Thirdness is the mode of being of that which is such as it is, in bringing a second and a first into relation.”

Peirce’s category of Thirdness names mediation, lawfulness, and intelligible continuity. It points beyond dyadic relations to the conditions under which relations can be meaningful at all.

Aristotle, Metaphysics Γ.4 (1006a)
τὸ αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον

“It is impossible for the same thing to belong and not belong to the same thing at the same time.”

The principle of non-contradiction is not derived from a system; it governs the possibility of systemhood itself.

Explicatio

The inquiry into metalanguage arises not from philosophical curiosity but from the internal limits of formalization itself. Whenever a formal system is sufficiently expressive to represent arithmetic, syntax, or inference, it becomes possible to ask questions about the system as a system: about its consistency, its completeness, its interpretability, and its truth conditions. These questions are not posed within the object language alone but from a vantage that speaks about the system. This vantage is meta-discourse.

Gödel’s incompleteness theorems make this structural distinction unavoidable. The encoding of syntactic relations by Gödel numbering allows statements about provability to be represented within arithmetic. Yet the recognition of undecidable truths still requires a standpoint that distinguishes truth from provability. That distinction is not eliminable. Even when meta-statements are formalized, the act of recognizing the adequacy of that formalization occurs at a higher level still. The meta recedes as it is formalized. What is gained in rigor is offset by a renewed excess.

This phenomenon is not accidental. It reveals something essential about intelligibility itself. Formal systems can model relations, generate derivations, and define extensions. What they cannot do is generate the conditions under which their own operations are meaningful. The possibility of interpretation is not a theorem of the system; it is the horizon within which the system can appear as intelligible at all.

This horizon is not merely epistemic. It is not simply a limitation of human cognition or a defect in symbolic manipulation. It belongs to the nature of formal structures themselves. A system that could exhaustively account for its own intelligibility would collapse the distinction between object language and metalanguage, thereby eliminating the very conditions that make interpretation possible. Meaning would be flattened into mechanism, and truth into derivability.

To say this is not to disparage formal rigor. On the contrary, it is formal rigor that reveals the necessity of this distinction. Logic itself teaches that intelligibility cannot be fully objectified without remainder. The meta is not an embarrassment to formalism; it is its condition.

This irreducible excess may be clarified by reconstructing Peirce’s notion of Thirdness. Thirdness is not merely a category of mediation within thought. It names the lawful continuity that makes relations intelligible. It is that by virtue of which signs signify, laws govern, and inference is possible. In this sense Thirdness is not added to dyadic relations; it is what allows relations to be relations rather than brute collisions.

What Peirce names phenomenologically, we may here name ontologically. The intelligibility that coordinates formal systems is not imposed from outside but belongs to the structure of reality. Formal systems are not self-originating. They are drawn into being by the possibility of meaning that precedes them. This possibility is not itself formal, yet it is not indeterminate. It orders, constrains, and directs formalization without being reducible to it.

Whitehead’s notion of prehension may serve as an analogy. Prehensions are not actual entities but the permanent possibilities of actualization. They are not events but the conditions under which events can occur meaningfully. In an analogous way, intelligibility is not itself a formal structure but the permanent possibility of formal meaning. It is that by which formal systems can be interpreted, related, and evaluated.

This is why attempts to algorithmize theory change inevitably fail. To formalize the rules by which theories are revised presupposes a prior understanding of relevance, adequacy, and success—concepts that themselves resist algorithmic capture. The criteria of revision always exceed the system being revised. The ladder by which the system ascends cannot be retained within the system without contradiction.

Wittgenstein’s Tractatus gestures toward this limit. What cannot be said must be shown. Yet showing is not mute. It is a mode of intelligibility that precedes explicit articulation. There is no seeing that could not, in principle, be spoken—but the speaking presupposes the very space it attempts to articulate. The ladder cannot be climbed unless it already stands.

Kant’s distinction between determining and reflecting judgment clarifies this further. Determining judgment subsumes particulars under given rules. Reflecting judgment seeks the rule under which particulars may be unified. The former may be formalized. The latter resists algorithmic closure. Reflecting judgment operates within a teleological space: it seeks coherence, purposiveness, and meaning without presupposing a determinate schema. This space is not subjective whim. It is the condition under which object languages can be coordinated at all.

Thus intelligibility is teleological not because it aims at a humanly imposed end, but because it orients formal structures toward meaning. Formal systems are “pulled into being” by this space. They do not emerge ex nihilo. They are responses to a prior call of intelligibility that is written into the structure of reality itself.

Objectiones

Ob I. If intelligibility exceeds formal systems, then rigor is compromised and mathematics collapses into metaphysics.

Ob II. Metalanguage reflects only human cognitive limitation, not any ontological feature of reality.

Ob III. Teleology introduces purpose into domains governed solely by efficient causality.

Ob IV. If intelligibility cannot be formalized, then it cannot be known or discussed without contradiction.

Responsiones

Ad I. Rigor is not compromised but clarified. Formal precision reveals the limits of formalization. To acknowledge these limits is not to abandon rigor but to respect its conditions.

Ad II. The recurrence of metalanguage is not contingent upon human psychology. It arises from the structure of formal systems themselves. Any intelligence capable of truth would confront the same distinction.

Ad III. Teleology here names orientation toward meaning, not extrinsic purpose. It does not replace efficient causality but grounds the intelligibility of causal explanation.

Ad IV. Intelligibility can be discussed analogically and architectonically without being reduced to an object language. Such discourse does not eliminate the meta; it inhabits it knowingly.

Nota

This disputation marks a decisive transition within the Disputationes. Up to this point, the inquiry has examined language, truth, causality, participation, and manifestation within the horizon of theological speech. Here the investigation turns explicitly to the conditions under which any discourse—logical, scientific, or theological—can be intelligible at all.

The significance of Gödel’s results is not exhausted by their mathematical application. They reveal that truth is not coextensive with formal derivability and that intelligibility requires a standpoint irreducible to object language. This insight aligns logic with philosophy at its deepest level. Logic does not eliminate metaphysics; it summons it.

The reconstruction of Peircean Thirdness offered here is not semiotic but ontological. It prepares the way for a theology of intelligibility by showing that meaning is not a human projection but a feature of reality. Formal systems respond to intelligibility; they do not create it.

This recognition quietly undermines every reductionist account of reason. It shows that the space in which meaning arises is not manufactured by minds but discovered by them. The humanities and mathematics converge here, not in method but in vocation: both seek the conditions of intelligibility.

Theological implications are now unavoidable, though not yet asserted. If intelligibility belongs to the structure of reality, then meaning is not accidental. If meaning is not accidental, then the question of Logos presses itself forward—not as hypothesis, but as the name for the ground of intelligibility itself.

Determinatio

1. Formal systems presuppose intelligibility and do not generate it.

2. No sufficiently expressive system can internalize the conditions of its own truth.

3. The distinction between object language and metalanguage is irreducible.

4. This irreducibility is ontological, not merely epistemic.

5. Intelligibility constitutes a teleological space of meaning.

6. Formal systems are drawn into being by this space rather than constituting it.

Transitus 

If the intelligibility of formal systems presupposes an irreducible metadiscursive horizon, and if this horizon is not merely epistemic but grounded in the being of things themselves, then intelligibility cannot be understood as an accidental feature of formalization. It belongs instead to the structure of reality as ordered toward meaning.

What has now emerged is the necessity of law—not yet as a catalog of determinate principles, nor as primitive axioms internal to any one system, but as the ontological condition under which intelligibility may take stable, communicable form. Formal systems do not generate this order; they respond to it. They are drawn into articulation by a prior normativity that renders meaning possible and truth answerable.

The question therefore presses beyond the limits of metalinguistic excess toward the nature of order itself. How is intelligibility stabilized without being exhausted? How does teleological attraction give rise to lawfulness without collapsing into mechanism or necessity? And in what sense may laws be said to participate in the very ground of intelligibility they articulate?

These questions compel the inquiry to move from the conditions of meaning to the structures of order by which meaning abides. We therefore turn to the consideration of law—not as an artifact of formal reason, but as a mode of being through which intelligibility is sustained and made communicable.

Authorial Note on the Proceeding Disputations

Over the past two months I have posted 64 disputations. They must seem to many to be difficult or just odd, for I use Latin titles and deal with some rather technical issues. What am I trying to accomplish by posting these in rapid fire order? 

Actually, these disputationes were composed over the course of many years, often in the margins of administrative work, teaching, and the founding of an institution devoted to theological truth. They reflect not only the content of my research but the shape of my vocation. The scholastic form became for me not a historical curiosity but a discipline that ordered my own thinking when the theological landscape around me seemed increasingly fragmented.

I posted these dispuations in the spirit of theological transparency. While they are not yet in final form, they are ready to take off the desk and circulate to friends and colleagues. I do care about any responses anybody might have to these, and will likely modify the posts in response to feedback. My hope is to speak clearly, and sometimes this is a difficult task for the theologian. These revised disputations will ultimately constitute a new book, Disputationes Theologicae: Sixty-Four Exercises in Theological Reason, that I hope to bring out in 2026. 

The questions addressed here emerged from two lifelong commitments: first, to the reality of God’s action in the world; and second, to the conviction that theology must speak truthfully about that action. Much of modern theology has relinquished metaphysics, often on the assumption that metaphysical claims are speculative or oppressive. But I found, in study and in prayer, that theology without metaphysics cannot speak coherently of divine presence, incarnation, sacrament, Spirit, or resurrection. These disputationes are therefore an attempt to recover, without nostalgia, the ontological depth that the Christian tradition presupposed.

They are also marked by the life of the Institute of Lutheran Theology, where theology is lived before it is written. The work of building an institution taught me that theology is not merely conceptual but performative—that truth animates communities as well as texts. Many of these disputationes were written in the quiet hours after long days of work, when the only thing that could be done was to write toward clarity.

I offer them to the reader with gratitude. If they serve to strengthen theological intelligence, deepen participation in Christ, or clarify the hope that sustains the Church, then their purpose will have been fulfilled.

D. B.

Advent II
Sioux Falls, SD

Disputatio LXIV: De Spe et Resurrectione

On Hope and Resurrection

Quaeritur

Utrum spes Christiana fundamentum habeat in ipsa structura participationis, ita ut resurrectio non sit extrinseca recompensatio sed consummatio participationis in vita Dei; et quomodo Spiritus identitatem personalem per mortem servet et restituat, ita ut resurrectio sit opus remembrance divinae potius quam naturae humanae.

Whether Christian hope finds its foundation in the very structure of participation, such that resurrection is not an extrinsic reward but the consummation of participation in the life of God; and how the Spirit preserves and reconstitutes personal identity through death, so that resurrection is an act of divine remembrance rather than a natural extension of creaturely being.

Thesis

Resurrection is the eschatological manifestation of participation. What is now hidden—participation in the crucified and risen Christ—will then be revealed as the definitive form of life. Hope is therefore not the anticipation of a future possibility but the confident trust that the Spirit who has begun participation will bring it to completion. The believer’s identity is preserved through death not by the persistence of a metaphysical substrate but by the fidelity of divine remembrance. Resurrection is God’s act of reconstituting the person in the fullness of life by the same power that raised Christ from the dead.

Thus the Christian does not hope for escape from finitude but for the transfiguration of finitude into glory.

Locus Classicus

1 Corinthians 15:20–22
νυνὶ δὲ Χριστὸς ἐγήγερται ἐκ νεκρῶν… ὥσπερ γὰρ ἐν Ἀδὰμ πάντες ἀποθνήσκουσιν, οὕτως καὶ ἐν τῷ Χριστῷ πάντες ζωοποιηθήσονται.
“Christ has been raised from the dead… for as in Adam all die, so in Christ shall all be made alive.”

Romans 8:11
ὁ ἐγείρας Ἰησοῦν ἐκ νεκρῶν ζωοποιήσει καὶ τὰ θνητὰ σώματα ὑμῶν διὰ τοῦ ἐνοικοῦντος πνεύματος.
“He who raised Jesus will give life also to your mortal bodies through His indwelling Spirit.”

Luther, WA 10 I, 1, 45
Resurrectio est opus purum Dei, qui nos de nihilo iterum creat.
“Resurrection is the pure work of God, who creates us again out of nothing.”

Explicatio

1. Participation is the seed of resurrection

Participation is not merely moral renewal or spiritual elevation. It is the ontological union of the believer with the crucified and risen Christ through the Spirit. This participation is incomplete and hidden under the conditions of mortal life, but it bears within itself the form of its fulfillment. Resurrection is the revelation of what participation already is: life sustained by the Spirit, grounded in Christ, embraced by the Father.

Thus hope is not conjecture. It is the anticipation of what participation necessarily entails.

2. Death as the boundary at which creaturely agency ceases

Death is not merely the cessation of biological functions. It is the interruption of creaturely self-articulation. The creature can no longer enact its identity. All natural continuity fails. If the person is to persist, it must be through a form of identity not grounded in creaturely endurance but grounded in divine fidelity.

This is why hope is theological, for the creature cannot secure its own future. Only God can remember and reconstitute the creature.

3. Divine remembrance as the ground of personal identity

Identity is not an inert substance but a pattern of intelligibility sustained by the Spirit. In life, the Spirit shapes the believer into conformity with Christ. In death, the Spirit retains this pattern in divine remembrance. In resurrection, the Spirit reconstitutes the believer according to this remembered form.

Thus the believer’s identity does not persist by nature. It persists because the Spirit is faithful.

This is Luther’s insight: God remembers the person into being.

4. Resurrection as the consummation of cruciform participation

Because participation is cruciform—shaped by the humility and majesty of the crucified Christ—resurrection must be the revelation of this form in glory. Glory is not a reversal of the cross but its fulfillment. The wounds of Christ are not erased; they become radiant. In resurrection, creaturely life is purified of distortion but not stripped of finitude. The creature remains creature, yet its life is transfigured by union with the Logos.

5. Eschatological hope is grounded in the Spirit’s constitutive causality

Hope is not grounded in the autonomy of the soul but in the Spirit’s power to give life. Romans 8:11 is decisive: resurrection occurs διὰ τοῦ ἐνοικοῦντος πνεύματος—through the indwelling Spirit.

Thus:

• Christ is the form of resurrection,

• the Spirit is the cause of resurrection,

• the Father is the source of resurrection.

Participation is therefore Trinitarian in its origin, structure, and consummation.

6. Resurrection is not the natural immortality of the soul

Natural immortality cannot sustain the theological hope of resurrection. It reduces eschatology to anthropology and empties the cross of its metaphysical significance. The Christian does not hope for the survival of a separable essence. The Christian hopes for the recreation of the person by the God who raises the dead. Thus Luther reminding us that God makes something out of nothing. Clearly, resurrection is precisely this nothing-from-something again.

Objectiones

Ob I. If identity depends on divine remembrance, does this not destroy continuity of person?

Ob II. If resurrection is pure divine act, how can the believer’s moral history matter?

Ob III. Does this not reduce eschatology to determinism?

Ob IV. How can the risen body be both continuous with the mortal body and glorified?

Ob V. Does the hope of resurrection undermine the seriousness of death?

Responsiones

Ad I. Divine remembrance is not recollection but constitutive fidelity. The person remains the same because God preserves the pattern of intelligibility that defines the person. Continuity is secured at the highest possible level.

Ad II. Moral history matters because God remembers the person as the person has been shaped in Christ. Resurrection does not erase moral history; it redeems and completes it.

Ad III. Resurrection is certain, but it is not deterministic. It is the consequence of divine promise, not metaphysical compulsion. Hope rests on fidelity, not necessity.

Ad IV. Continuity lies in identity; transformation lies in glory. The mortal body is raised immortal because the Spirit reconstitutes it according to its true form in Christ.

Ad V. The seriousness of death is intensified, not diminished. Death destroys every creaturely ground of hope so that hope may rest entirely in God.

Nota

Resurrection is the final act of the participatory ontology developed throughout these disputations. It is the Spirit’s definitive articulation of the believer in conformity to Christ. It is not the resumption of interrupted life but the gift of new life. Hope is therefore the posture of those who know that their future lies not in their own endurance but in the God who raises the dead.

Determinatio

We determine that resurrection is the eschatological fulfillment of participation in the life of God. Death cannot sever the believer from Christ because the Spirit preserves personal identity through divine remembrance. Resurrection is God’s reconstitution of the creature in glory, revealing the cruciform form of divine life in perfected clarity. Hope rests not in natural immortality but in divine fidelity. The final word of theology is therefore not abstraction but promise: the love that made us will remake us.

Finis

Epilogus: De Fine Theologiae et Forma Vitae

The sixty-four disputationes have traced a path across the full horizon of theological reason. We began with logic, not because theology is reducible to logical form, but because theology must speak intelligibly of what it confesses. We proceeded to ontology, not because metaphysics precedes revelation, but because divine revelation presses thought to articulate what it has seen. We turned to Christology, where intelligibility and being converge in the Logos who is both the form of God and the form of the servant. We explored the Spirit’s illumination, creaturely participation, providence, history, cruciformity, and finally the hope of resurrection.

Through all of these movements a single conviction has guided the work: theology speaks truly only because God acts. Theological speech is not the construction of a conceptual system, nor the refinement of human religious insight, nor the self-expression of a community. It is the response of reason awakened by divine presence. Theology is an act of participation: the mind caught up into what it cannot generate but can only receive.

Thus each disputatio—however analytic in method or metaphysical in structure—has aimed to keep before the reader the living center of theological truth: the God who gives Himself to be known. The Logos renders divine life intelligible. The Spirit renders this intelligibility accessible. The Father is the eternal source of both. Without this triune economy of self-giving, the work of theology collapses either into rationalization or despair.

The communicatio idiomatum stands at the heart of this vision, for in Christ God shows not only who He is but how He acts. The hypostatic union is not an isolated miracle but the grammar of all divine–human communion. It grounds the real presence in sacrament, the efficacy of the Word, the transformation of the believer, and the final hope of resurrection. What Christ is personally, believers become participatively. This is the shape of grace.

The cross reveals the form of this grace. Divine majesty appears in humility, not by contradiction but by nature of divine love. In the crucified Christ the character of God is made manifest: power exercised as mercy, glory revealed in self-offering. All genuine theological understanding must therefore pass through the cruciform horizon. Outside the cross, divine majesty becomes a metaphysical abstraction or an instrument of human pride. In the cross, majesty becomes the world’s redemption.

This is why the final disputatio turns to hope. Resurrection is not the compensation for suffering nor the restoration of natural capacities but the consummation of participation. What the Spirit has begun in the believer—conformity to the form of the Son—He completes in the act of divine remembrance. The Christian does not place hope in the durability of the soul but in the fidelity of God. To be remembered by the God who raises the dead is to live forever.

If these disputationes have any unity, it lies here: theology is the mind’s participation in God’s self-giving act. It proceeds from revelation, through illumination, into understanding, and finally to praise. Its method is disciplined, its language careful, its categories precise, but its end is doxological. Theology thinks because God speaks; theology understands because God gives; theology hopes because God remembers.

The disputationes end where theology always ends; they end in the confession that the love that made us will remake us and that the last word spoken over all creaturely life is not death but the Word Himself.

Soli Deo Gloria

Disputatio LXIII: De Maiestate Crucis et de Forma Humilitatis Divinae

 On the Majesty of the Cross and the Form of Divine Humility

Quaeritur

Utrum crux Christi manifestet non solum humiliationem Filii sed ipsam maiestatem divinam in forma humilitatis, ita ut crux sit locus in quo genus maiestaticum et genus tapeinoticum maxima intensitate convergunt; et quomodo haec paradoxica unitas revelet formam participationis qua creaturae per Spiritum transformantur.

Whether the cross of Christ manifests not only the Son’s humiliation but also divine majesty in the form of humility, such that the cross becomes the locus where the genus maiestaticum and the genus tapeinoticum converge in maximal intensity; and how this paradoxical unity reveals the form of participation by which creatures are transformed through the Spirit.

Thesis

The cross is the supreme manifestation of divine majesty. It is not merely the site of Christ’s suffering but the revelation of the divine form as self-giving love. Humiliation is not the concealment of majesty but its mode of appearing to the fallen world. In the crucified Logos, the genus tapeinoticum becomes the visible form of the genus maiestaticum. Divine glory assumes the shape of weakness so that the creature may be drawn into communion without annihilation.

Thus the cross is not a negation of divine power but the definitive expression of divine action. Participation in God is necessarily cruciform: the Spirit conforms believers to the form of the Son precisely in His self-emptying, wherein divine majesty radiates as mercy.

Locus Classicus

Philippians 2:6–8
ὃς ἐν μορφῇ Θεοῦ ὑπάρχων… ἑαυτὸν ἐκένωσεν μορφὴν δούλου λαβών… γενόμενος ὑπήκοος μέχρι θανάτου, θανάτου δὲ σταυροῦ.
“Who, being in the form of God… emptied himself, taking the form of a servant… becoming obedient unto death, even death on a cross.”

Isaiah 53:2–3 (Vulgate)
non est species ei neque decor… et quasi absconditus vultus eius.
“He has no form or beauty… his face is hidden.”

Luther, WA 5, 162
Crux sola est nostra theologia.
“The cross alone is our theology.”

Explicatio

1. The form of God as the form of servanthood

Paul’s language of morphē Theou and morphē doulou does not describe two disconnected states. The latter is the revelation of the former. The divine form—ungrasping, self-giving—is disclosed precisely in the assumption of servanthood. Humiliation is the visibility of divine majesty.

This reverses all metaphysical expectations grounded in natural reason. One expects glory to appear in splendor; it appears in dereliction. One expects divine power to manifest in domination; it manifests in self-offering. The cross therefore reveals the true form of divine action: love that gives itself for the other.

2. The genus tapeinoticum as revelatory, not merely economic

The tapeinoticum is not simply the narrative reality that Christ suffers as man. It is the metaphysical reality that the divine person bears suffering as His own. This is why the Fathers insisted: unus ex Trinitate passus est.

Humiliation is not external; it is hypostatic.The Logos does not appear lowly. The Logos becomes lowly.
Yet this lowliness is itself the expression of divine majesty. Here the genus tapeinoticum is not the negation of the maiestaticum but its visibility.

3. The majesty of God hidden in weakness

Luther’s theology of the cross is not a theological preference but a metaphysical insight. Divine glory is hidden under its opposite not by accident but by nature of divine love. If glory appeared directly as power, humanity would be destroyed. If power appears as weakness, humanity is redeemed.

This is the ontological core of Luther's sub contrario: God is most present where He seems most absent. God is most powerful where He seems most weak. God is most glorious where He seems most forsaken. The cross is therefore the form of God.

4. The cross as the integration of the genera

Here the genera meet:

• Genus idiomaticum: The one who dies is God.

• Genus tapeinoticum: The divine person bears human lowliness.

• Genus maiestaticum: The divine life is present in the very act of dying.

• Genus apotelesmaticum: The work of redemption is accomplished by the united action of one divine–human agent.

No nominalist grammar can sustain this. Only an ontological communicatio—real, hypostatic, participatory—can bear the weight. The cross is therefore the maximal expression of Christological ontology.

5. Participation as conformity to cruciform majesty

If the cross reveals the form of God, and if believers participate in divine life, then participation is necessarily cruciform. The Spirit conforms believers not to abstract majesty but to majesty revealed in humility. Recall Romans 8:29: συμμόρφους τῆς εἰκόνος τοῦ Υἱοῦ (“Conformed to the form of the Son.”)

This conformity is not psychological alone. It is metaphysical: a shaping of the believer’s agency by the Logos through the Spirit. Participation is suffering-formed and resurrection-bound. For Luther, the cross is not one stage among others. It is the shape of Christian life and the intelligibility of divine action.

Objectiones

Ob I. If the cross is divine majesty, does this not negate the very meaning of majesty?

Ob II. How can divine impassibility be preserved if the Logos suffers?

Ob III. Does cruciformity impose suffering as a metaphysical necessity upon the believer?

Ob IV. Does this not reduce divine power to moral influence?

Ob V. If glory is hidden, how can it be recognized without contradiction?

Responsiones

Ad I. Majesty is not domination but self-giving. The cross does not negate majesty but expresses its deepest character.

Ad II. The impassible divine nature does not suffer; the divine person suffers in the human nature. This is the communicatio idiomatum. Impassibility and passion coexist hypostatically without confusion.

Ad III. Cruciform participation does not mean perpetual suffering but conformity of will to divine self-giving. Suffering is not the goal; love is. Suffering is its historical mode.

Ad IV. Divine power is not diminished but intensified in the cross. It accomplishes what no coercion can: the reconciliation of the world.

Ad V. Glory is recognized through illumination. The Spirit reveals the hidden majesty of the crucified Christ. Without illumination, the cross appears as folly.

Nota

The cross stands at the heart of theological ontology. It reveals the structure of divine action and the mode of participation. The metaphysics of humility is the metaphysics of glory. What nominalism cannot grasp—because it denies real communication—Luther perceives: God’s majesty is not compromised by humiliation; it is unveiled in it. The cross is the radiant depth of divine being.

Determinatio

We determine that the cross is the definitive revelation of divine majesty, not its negation. The genus tapeinoticum and genus maiestaticum converge in the crucified Logos, revealing divine glory in the form of humility. This cruciform majesty is the basis of all participation: the Spirit conforms believers to the form of the Son so that they may share His life. The cross is the metaphysical center of divine self-giving and the existential form of participation in God.

Transitus ad Disputationem LXIV

Having shown that divine majesty is revealed in the crucified form, we now turn to the final horizon where this form is perfected: resurrection and hope. Participation reaches its eschatological fulfillment when the Spirit reconstitutes the believer’s identity through divine remembrance.

We therefore proceed to Disputatio LXIV: De Spe et Resurrectione.