§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
3.1. Reflexivity and Its Variants
A relation is:
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Reflexive iff (∀x ∈ D)Rxx
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Non-reflexive iff ~(∀x ∈ D)Rxx
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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 is:
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Symmetric iff (∀x ∈ D)(∀y ∈ D) (Rxy → Ryx)
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Non-symmetric iff ~(∀x ∈ D)(∀y ∈ D)(Rxy → Ryx)
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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 is:
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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 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:
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Equivalence relation: reflexive, symmetric, transitive
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Strict partial order: irreflexive, transitive
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Partial order (poset): reflexive, antisymmetric, transitive
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Total (linear) order: partial order plus connectivity
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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:
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Dependence: a structural priority relation
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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.
