Basic Intelligibility, Teleo-Spaces, and the Discipline of Sense (Reading Wittgenstein's Tractatus 1:0 - 3.5)

 I. The Problem of Basic Intelligibility

Any philosophy that takes itself seriously must eventually confront a question that is almost never stated with sufficient clarity: why is anything intelligible at all?

This is not the familiar question of why particular propositions are true, nor why certain inferential practices succeed. It is the more basic question of why determinacy itself obtains—why distinctions hold rather than dissolve, why meaning does not collapse into either infinite regress or sheer indifference. One may explain this or that truth, but explanation already presupposes a field in which explanation can count as explanation. The deeper question concerns the possibility of sense as such.

Reflection shows that this question cannot be answered algorithmically. An algorithm already presupposes a distinction between correct and incorrect application and therefore operates within a prior space of intelligibility. Nor can the question be resolved by appeal to subjectivity, social practice, or convention, since these themselves function only insofar as distinctions already matter. Even formal logic cannot close the issue. Logic presupposes a field of possible sense in order to operate as logic at all. It does not generate that field.

To name this condition without prematurely domesticating it, I shall speak of teleo-space. A teleo-space is not an entity, a subject, or a hidden metaphysical layer. It is a structured field of intelligibility—one in which distinctions can obtain, norms can exert force, and direction toward sense can emerge without the prior imposition of explicit rules. Logical space is one such teleo-space, but it is not unique. Ethical, perceptual, and practical spaces exhibit the same basic structure. In each case, intelligibility is not conferred by a subject nor derived from convention; it is the condition under which judgment is possible at all.

The thesis hovering over this series can therefore be stated with restraint: regress in meaning, truth, and metaphysics does not terminate in silence, algorithm, or social practice, but in a basic, weighted intelligibility of reality itself. Whether this intelligibility is finally grounded in the Logos is not presupposed here. That question will emerge—or be resisted—under pressure from the texts themselves.

With that pressure in view, we turn to the Ludwig Wittgenstein's first book: The Tractatus Logico-Philosophicus. 

The World as Determinate (1.0–1.13)

Wittgenstein opens with a sentence that immediately enforces determinability:

1. Die Welt ist alles, was der Fall ist.
“The world is everything that is the case.”

The world is not the totality of what exists but of what obtains. This is already a restriction of intelligibility. What cannot be the case cannot be said, and what cannot be said does not enter the space of sense.

The point is sharpened immediately:

1.1 Die Welt ist die Gesamtheit der Tatsachen, nicht der Dinge.
“The world is the totality of facts, not of things.”

Facts, not objects, are the bearers of intelligibility. Objects do not explain sense; they participate in it only insofar as they occur in determinate configurations. An isolated “thing” is not yet meaningful. Sense requires articulation; it requires that something could be otherwise. What blocks regress here is not explanation but constraint.

Logical Space and Possibility (1.13–2.0122)

Wittgenstein then introduces logical space as the unified field in which facts are possible:

1.13 Die Tatsachen im logischen Raum sind die Welt.
“The facts in logical space are the world.”

Logical space is not constructed, inferred, or discovered. It is presupposed. One does not assemble intelligibility piece by piece; one always already operates within a field of possible sense.

This presupposition becomes explicit in the discussion of objects:

2.0121 Es wäre unmöglich, die Gegenstände zu denken, ohne sie in einem Sachverhalt denken zu können.
“It would be impossible to think of objects without thinking of them as occurring in states of affairs.”

Objects can only be thought as possibly occurring. Their independence is therefore modal rather than ontological:

2.0122 Das Ding ist selbständig insofern es in allen möglichen Sachlagen vorkommen kann.
“The object is independent in so far as it can occur in all possible situations.”

From the perspective of teleo-spaces, this is decisive. Objects are not intelligible on their own; they are nodes within a space of directed possibility. Any attempt to ground meaning in metaphysical atoms is thereby foreclosed. At the same time, the unity of logical space itself is presupposed rather than explained. It is enforced as a condition of sense.

Simplicity and the Arrest of Regress (2.02–2.0212)

Wittgenstein insists:

2.02 Der Gegenstand ist einfach.
“The object is simple.”

This simplicity is not empirical but logical. Objects mark where analysis must stop if meaning is to arrive at all. The reason is explicit:

2.0211 Wenn die Welt keine Substanz hätte, so würde, ob ein Satz Sinn hat, davon abhängen, ob ein anderer Satz wahr ist.
“If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.”

If sense depended on further propositions, regress would be infinite. Meaning would never stabilize. Here Wittgenstein aligns fully with the teleo-space intuition: intelligibility cannot be deferred without limit. There must be a given field of determinability within which articulation can occur. What he refuses to do is explain why such a field holds together. He treats it as a condition of sense rather than an object of theory.

Picturing, Logical Form, and Showing (2.1–2.18; 2.172)

When Wittgenstein writes,

2.1 Wir machen uns Bilder der Tatsachen.
“We make to ourselves pictures of facts,”

Wittgenstein is not appealing to psychology. A Bild is a structured representation whose power lies not in mental imagery but in shared articulation. What every picture must share with reality is logical form:

2.18 Was jedes Bild … mit der Wirklichkeit gemein haben muss … ist die logische Form.
“What every picture must have in common with reality … is logical form.”

Logical form is not an object among others. It is the condition of representation itself. This is why it cannot be represented:

2.172 Das Bild kann seine logische Form nicht abbilden; es zeigt sie.
“The picture cannot represent its logical form; it shows it.”

What shows itself here is not ineffable content but unavoidable constraint. No formal system can state its own conditions of operation without circularity. No rule can generate the space in which it functions as a rule. This marks a decisive anti-algorithmic moment in the Tractatus. Wittgenstein blocks explanation precisely where intelligibility is doing its deepest work.

Tension and Orientation

Up through this point, Wittgenstein consistently affirms determinacy, blocks regress, rejects algorithmic closure, and denies subjectivist grounding. All of this converges with the claim that intelligibility is real, structured, and irreducible.

The tension emerges at the question of ground. Logical space is treated as a condition of sense that must be presupposed but not accounted for. The teleo-space framework insists that such presuppositions themselves demand ontological reckoning—not as entities or axioms, but as the condition under which determinacy can obtain at all.

Whether that reckoning must finally appeal to the Logos remains an open question. But the Tractatus ensures that the question cannot be avoided. It disciplines thought into seeing where explanation must stop—and where philosophy must either recoil or press forward.

That pressure is the work ahead.

Sense without Sense?

Quine, Carnap, and the Persistence of Intelligibility

The reflections that follow were occasioned by a recent paper by Lucas Ribeiro Vollet, “Sense (Sinn) as a Pseudo-Problem and Sense as a Radical Problem: A Reading of the Motivations of Quine against Carnap" (https://independent.academia.edu/s/c59ed03835). Vollet kindly invited comment on the piece, and it repays careful reading. The article revisits the familiar—but still unsettled—Quine–Carnap dispute over Sense, not as a merely historical episode, but as a diagnostic window into the limits of semantic theory in the twentieth century.

Vollet’s central claim is worth stating clearly at the outset. He argues that Quine’s skepticism about intensions is not eliminativist in the crude sense often attributed to him. Quine does not regard the question of Sense as a pseudo-problem in the way some moral or metaphysical notions are dismissed as meaningless. Rather, he believes the question is incorrectly framed. What Carnap treats as a semantic problem—the need for intensional identity conditions stronger than extensional equivalence—Quine reinterprets as a scientific and methodological challenge: the ongoing task of coordinating empirical investigation, theory revision, and socially stabilized paradigms of meaning.

As Vollet summarizes in his abstract, Quine’s naturalism applies skepticism about intensions not to deny the reality of the problem, but to expose its mislocation. The appeal to sense functions as a semantically dogmatic expression of a broader difficulty already present in scientific practice itself: the challenge of providing coherence to inquiry, securing rational consensus, and stabilizing paradigms of meaning over time. Vollet names this the radical problem generated by the idea of Sense.

This reframing is philosophically serious and historically sensitive. It resists the temptation to caricature Quine as a blunt extensionalist and instead situates his critique of sense within a broader vision of scientific rationality. There is much here with which one can agree. Yet the very sophistication of Vollet’s reconstruction also sharpens a question that neither Quine nor his interpreters fully resolve: what becomes of intelligibility once formal semantics has been dismantled, but scientific practice itself presupposes more than extensional structure can supply?

It is this question—rather than the fate of “sense” as a semantic object—that motivates what follows.

I. The Legitimate Collapse of Intensional Semantics

Quine’s central insight was not merely that intensional entities resist formal definition. It was that the criteria by which such entities were supposed to be individuated—analyticity, synonymy, necessity—could not be specified without circularity. Any attempt to regiment them either presupposed what it claimed to explain or relied on pragmatic judgments smuggled in under the guise of logical form.

Vollet is right to insist that this is not a technical oversight but a structural failure. There is no algorithm for sense. No calculus decides synonymy. No formal rule distinguishes what is merely coextensive from what is cognitively equivalent. To that extent, the Carnapian project fails decisively.

This failure should not be minimized. It forces a clean and non-negotiable distinction between what syntax can secure—derivability, consistency, inferential order—and what it cannot: meaning, reference, or truth. Formal rigor does not rescue sense; it exposes its absence as a formal object. Any attempt to recover sense by enriching syntax, appealing to semantic rules, or invoking linguistic frameworks only relocates the difficulty without resolving it.

In this respect, Quine’s critique remains one of the most important negative results of twentieth-century philosophy.

II. The Non Sequitur: From Failure to Elimination

Where the argument falters is in the inference drawn from this failure. Quine famously concluded that since intensional semantics cannot be formalized, there is no fact of the matter beyond extensional equivalence and the evolving practices of empirical science. Meaning becomes, at best, a byproduct of theory choice, pragmatic convenience, and holistic revision.

But this conclusion does not follow.

The failure of formal capture does not entail the unreality of what resists capture. It shows only that the object in question is not an object of the same kind as formal derivations or syntactic structures. To infer elimination from non-formalizability is to mistake a methodological limitation for an ontological verdict.

Indeed, Quine’s own account of scientific practice quietly depends on distinctions that extensionalism alone cannot generate. Theory revision is not arbitrary. Scientific change is constrained by judgments of relevance, coherence, explanatory power, and unification—none of which are derivable from extensional relations alone, and none of which can be dictated by data without remainder. These judgments are not internal to a theory in the way axioms are; nor are they reducible to convention. They presuppose a space in which theories can count as making better sense of a domain rather than merely succeeding instrumentally.

Quine identifies the failure of intensional semantics correctly. What he fails to identify is what that failure presupposes.

III. Intelligibility Without Intensions

Once sense is rejected as a formal intermediary, we are left with a striking alternative: intelligibility without intensional objects. The question is no longer What is the sense of this expression? but How is sense-making possible at all, if no formal structure can generate it?

Vollet gestures toward an answer by appealing to coordination, rational negotiation, and scientific practice. But these gestures remain descriptive rather than explanatory. They name sites where intelligibility is exercised without accounting for what makes such exercise possible in the first place.

Theory choice, interpretive adequacy, and conceptual revision all presuppose a non-formal orientation toward meaning. This orientation is not itself a theory, nor a rule, nor a convention. It is the condition under which theories, rules, and conventions can be assessed as intelligible rather than merely adopted.

This is the point at which extensionalism quietly depends on what it officially disavows. The rejection of sense does not eliminate the problem of meaning; it relocates it to a level that resists objectification.

IV. Determination and the Space of Orientation

What emerges here is not a new intensional entity, but a structural distinction: the distinction between determination and determinability. Formal systems determine relations within a domain. But the capacity for such determination—to count as relevant, adequate, or successful—depends on a space of orientation that is not itself formally determined.

This space is neither subjective nor sociological, though it is encountered through finite judgments. It does not dictate outcomes, but it orients inquiry toward intelligibility. It guides without necessitating. It grounds without competing with determinate structures.

Attempts to collapse this space into practice, convention, or revisionary habit fail for the same reason that intensional semantics failed earlier: they confuse the exercise of intelligibility with its condition. What is presupposed in every successful act of interpretation cannot itself be reduced to the history of such acts.

V. Translation, Stabilization, and a Persistent Remainder

A brief exchange following Vollet’s paper sharpens this point further. In response to a comment emphasizing the importance of language–metalanguage distinctions, translation procedures, and higher-order logical resources for reconstructing ontological commitments—especially in contemporary AI contexts—Vollet agrees that such distinctions are crucial. They allow ontological commitments to be reorganized through mapping rules that preserve predictive roles while revising theoretical vocabulary.

Yet Vollet also raises an important hesitation. Translation frameworks, he suggests, may not be the only way to model ontological stabilization. Fixed-point constructions, iterative self-mapping, and convergent computational paths might also generate stable ontological frameworks internally, without appeal to pre-given semantic foundations. From this perspective, intensional—or even “supersensible”—structures emerge as products of convergence rather than as metaphysical primitives. Quine, Vollet suggests, might allow such internal stabilization, provided it remains constrained by biological, social, or cultural selection pressures that guide coordination toward shared reference.

This exchange is illuminating precisely because it confirms the deeper issue. Whether one appeals to translation, fixed points, or convergence, the question remains the same: what makes stabilization intelligible as stabilization rather than mere iteration? What distinguishes convergence from coincidence, coordination from collapse, agreement from brute alignment?

No amount of internal reorganization can answer that question from within.

VI. A Limit Quine Cannot Cross

Quine was right to dismantle the myth of sense as a semantic object. He was wrong to suppose that nothing remains once the myth is dispelled. What remains is intelligibility itself—real, irreducible, and non-formal.

Extensional logic shows us, with remarkable clarity, what form can and cannot do. But it also shows us that meaning is not generated by form. It is presupposed by it. The recognition of this fact does not require a return to intensions. It requires acknowledging that intelligibility has an ontological ground that formal systems inhabit but do not produce.

To say this is not yet to speak theologically. But it is to arrive at a threshold. The problem of sense dissolves. The problem of intelligibility does not. And it is precisely at that point—where philosophy has exhausted its formal resources without collapsing into irrationalism—that a deeper account of meaning becomes unavoidable.

That account begins not with semantic enrichment, but with the recognition that the space in which meaning appears is itself grounded. 

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.

Disputatio LVIII: De Signo Theologico et de Forma Illuminationis

 On the Theological Sign and the Form of Illumination

Quaeritur

Utrum signum theologicum sit locus in quo intelligibilitas Logi efficitur praesens creaturis sub forma signi, ita ut revelatio non sit mera significatio sed manifestatio; et quomodo Spiritus efficit ut ista manifestatio fiat participabilis sine reductione signi ad nudam immanentiam.

Whether the theological sign is the locus in which the intelligibility of the Logos becomes present to creatures under the form of a sign, such that revelation is not mere signification but manifestation; and how the Spirit ensures that this manifestation is participable without reducing the sign to a merely immanent function.

Thesis

A theological sign is not a symbol that points beyond itself to a distant referent. It is a created form through which the Logos-constituted intelligibility of divine action becomes manifest in the finite. The sign is therefore not extrinsic to revelation but intrinsic to its economy.

The Spirit illumines the sign so that it becomes transparent to the divine act it mediates. Without the Spirit, the sign remains opaque, but with the Spirit, the sign becomes the medium of participation in the Logos’ intelligible presence.

Thus, theological signs do not merely convey information. They are the formal structures by which divine act becomes encounterable within creaturely horizons.

Locus Classicus

John 1:14
ὁ Λόγος σὰρξ ἐγένετο.
“The Word became flesh.”

The incarnation is the archetype of all theological signs whereby a finite form makes the locus of divine manifestation.

Romans 10:17
ἡ πίστις ἐξ ἀκοῆς.
“Faith comes from hearing.”

The word heard is not a bare sound but a Spirit-illumined sign that mediates divine action.

Luther, WA 30 II, 552
Verbum Dei est signum et donum simul.
“The Word of God is both sign and gift.”

Theological signs participate in and deliver the reality they signify.

Explicatio

There is an insufficiency of semiotic models when detached from ontology. Modern accounts of signs often conceive signification as a relation between finite items: a signifier and a signified linked through convention or structure. While such accounts illuminate language, they cannot account for revelation. They lack a metaphysics of divine act and therefore reduce theological signs to linguistic functions. But revelation requires more than reference. It requires manifestation: the presence of divine intelligibility in a created medium. Thus the theological sign is not a semiotic function but a metaphysical participation.

The Logos is the form of every theological sign. Every divine act is intelligible because its form subsists in the Logos. Therefore every sign that mediates divine action must be a form shaped by the Logos. The sign does not merely refer to divine act but bears its intelligibility. Accordingly, the sign’s structure reflects the Logos’ form. Its content is not autonomous from divine initiative and its intelligibility is never self-standing but derivative upon the divine act. The incarnation is the paradigmatic case of this. But Scripture, sacrament, and promise share the same logic: each is a finite form bearing the intelligible presence of the Logos.

Illumination makes the sign participable. Without illumination, the sign remains closed. It does not disclose God, but merely displays creaturely form. Illumination opens the sign to become the medium of divine manifestation. This opening is not an epistemic alteration but an ontological donation. The Spirit grants creatures to encounter the divine act in and through the sign’s form. Knowledge arises because the sign becomes transparent to the Logos. Thus, illumination does not add meaning to the sign. It grants participation in the meaning the sign already bears.

The sign is an event rather than a static object. Theological signs are not static entities awaiting interpretation, but are rather events in which divine action becomes present. A sacrament is not an object but an enacted sign; Scripture is not merely text but living word; proclamation is not a speech-act alone but a site of divine address. The sign is therefore not exhausted by its linguistic or material properties. It is a finite locus of manifestation, rendered such by the Spirit who actualizes the Logos’ intelligibility within it.

The we must reject purely linguistic or immanent models. Postliberal theology sometimes construes revelation as emerging from within the grammar of the community. But the sign’s power does not lie in communal usage. It lies rather in divine action. The sign becomes revelation not when it is interpreted but when it is illumined. In this way, grammar orders discourse, while illumination grants reality. Thus, theological signs are not cultural artifacts whose meaning is negotiated, but are divine gifts that disclose.

Objectiones

Ob I. If signs mediate divine action, do we not reintroduce a created intermediary between God and creatures?

Ob II. If the Logos is the form of the sign and the Spirit the illuminator, is revelation split between form and access?

Ob III. If signs manifest divine act, does this collapse transcendence into immanence?

Ob IV. If illumination is necessary, how can signs retain objective meaning independent of subjective experience?

Ob V. If signs are events, does this undermine their stability or repeatability?

Responsiones

Ad I. Signs are not intermediaries but media. They do not stand between God and creatures but are the places where God acts. Their existence does not obscure God but reveal him.

Ad II. Revelation is not divided but ordered. The Logos shapes the sign’s intelligibility; the Spirit grants communion with this intelligibility. This expresses personal distinction, not division.

Ad III. Manifestation is not collapse. The finite does not contain the infinite. It is the locus where the infinite acts. Signs render God present without confining him.

Ad IV. Objective meaning arises from divine action, not from human consciousness. Illumination concerns reception, not constitution. The sign’s meaning is objective because its form is Logos-shaped.

Ad V. The sign’s repeatability arises from the constancy of divine intention. Its event-character does not eliminate stability but secures it: the same divine agent acts in each instantiation.

Nota

The theological sign is the place where divine intelligibility enters the finite economy under a form appropriate to creaturely reception. Its meaning lies neither in human interpretation nor in semiotic structures but in the Logos-shaped intelligibility that the Spirit illumines.

Thus theological signs cannot be reduced to texts, symbols, or practices. They are the finite forms through which God gives himself to be known.

Determinatio

We therefore determine:

1. Theological signs are finite forms made the loci of divine manifestation.
2. Their intelligibility is constituted in the Logos.
3. Their participability is granted by the Spirit.
4. Illumination does not alter the sign but opens it.
5. The sign mediates divine action not as representation but as presence.

Revelation is thus the event in which God’s intelligible act becomes manifest through a sign illumined by the Spirit.

Transitus ad Disputationem LIX

Having shown that theological signs mediate divine intelligibility through Spirit-illumined manifestation, we now turn to the economy of divine presence as it unfolds in history. For signs do not appear in abstraction but in a temporal order shaped by divine intention.

We proceed therefore to Disputatio LIX: De Historia Ut Loco Revelationis, where we consider how historical events become theological loci when illumined by the Spirit and formed by the Logos.

________

Quaestiones Analyticae Post Determinationem II

Q1. If a theological sign is a locus of manifestation rather than a semiotic relation, how does this relate to classical truth-conditional semantics?

Responsio

Truth-conditional semantics presumes propositional form. But theological signs precede propositional articulation. They provide the ontological ground upon which propositions can later be formed. The sign is not true or false; it is the site where divine action becomes manifest. Propositions about the sign acquire truth conditions only by referencing this manifestation.

Q2. Can theological signs be modeled within a hyperintensional semantics?

Responsio

Only analogically. Hyperintensionality captures distinctions finer than necessary equivalence, which is appropriate for theological signs whose meaning depends on participation, not extension. Yet signs exceed hyperintensional analysis because their identity lies not in conceptual structure but in divine act. Hyperintensional models can represent distinctions between interpretations but cannot constitute the reality they signify.

Q3. How does illumination relate to felicity conditions in theological discourse?

Responsio

Felicity pertains to the internal grammar of theological assertion. Illumination pertains to the external truth of what is asserted. A statement is felicitous when it accords with the grammar of faith; it is true when it corresponds to the Logos-constituted reality that the sign manifests. Illumination bridges the two by granting access to the reality that grounds felicity.

Q4. Do sacramental signs require a unique model-theoretic treatment?

Responsio

Yes. Sacramental signs are not merely designators but enactments. They cannot be captured by classical satisfaction (M ⊨ T). They require constitutive satisfaction (Λ ⊨* Tₜ), in which the divine act grounds both the sign and its efficacy. The model is not interpretive only; it is participatory.

Q5. If signs are events, does this eliminate the possibility of stable theological models?

Responsio

No. Events are stable insofar as the agent who performs them is stable. The constancy of divine intention grounds the repeatability of sacramental and scriptural signs. Stability in theology arises not from static forms but from the fidelity of the acting God.

Nota Finalis

This analytic section clarifies that theological signs occupy a space where ontology, semiotics, and logic converge. They resist reduction to any one of these domains. Their meaning is grounded in divine action, their form in the Logos, and their reception in the Spirit. This provides the conceptual foundation for the next disputation, where historical events become loci of revelation.

Disputatio LIV: De Hyperintensionalitate Divinae Operationis:

 

On the Hyperintensionality of Divine Action

Quaeritur

Utrum actus divini, quoad identitatem, formam, et rationem essendi, non possint explicari per extensionalem aequivalentiam, modalem necessitationem, vel possibilia mundorum, sed sint essentialiter hyperintensionales; et utrum veritas theologica requirat talem hyperintensionalitatem ut Deus cognoscatur secundum actum, non secundum eventum.

Whether the identity and form of divine acts can be explained by extensional equivalence, modal necessity, or possible-world semantics, or whether they are essentially hyperintensional; and whether theological truth requires such hyperintensionality so that God is known according to the act God performs, not merely according to an outcome.

Thesis

Divine acts are hyperintensional. By this we mean that the identity of a divine act cannot be captured by any framework in which acts are considered the same whenever they yield the same outcomes, share the same extension, or hold necessarily across all possible worlds. A divine act is not defined by its effects, nor by the set of circumstances under which it occurs, nor by its modal profile. Instead, a divine act is individuated by its formal identity within the Logos, by the specific constitutive act through which the Logos brings a res into being or presence, and by the Spirit’s concrete donation of that act to creatures.

Thus, extension does not capture divine identity,modal equivalence does not capture divine identity, and possible-world semantics is too coarse-grained to describe divine agency. A hyperintensional account alone preserves the theological conviction that God’s acts are personal, irreducible, and internally differentiated modes of the one divine life.

Locus Classicus

1. Exodus 3:14 — אֶהְיֶה אֲשֶׁר אֶהְיֶה

“I AM WHO I AM.”

This is not a definition, but an identity of act. Being itself is hyperintensional, for it names a unique form of divine acting, not a property instantiated across possible worlds.

2. John 5:19 — ἃ ἂν ἐκεῖνος ποιῇ, ταῦτα καὶ ὁ Υἱὸς ὁμοίως ποιεῖ

“Whatever the Father does, the Son does likewise.”

The divine act is not duplicated or numerically separable. Rather, its identity is internal to the Trinity, not extensionalized in effects.

3. Athanasius, Contra Arianos I.21

ὁμοούσιος οὐ κατὰ θέλησιν ἀλλὰ κατὰ φύσιν.
“Of one being not by will but by nature.”

The divine act is identical with divine being; it is an identity finer than any modal equivalence.

4. Gregory of Nyssa, Ad Ablabium

Οὐ τὰ γινόμενα, ἀλλ᾽ ὁ τρόπος τῆς ἐνεργείας τὴν διαφοράν ποιεῖ.
“It is not the outcomes, but the manner of operation that makes the distinction.”

This is a classical statement of hyperintensionality clearly stating that the manner by which something obtains profoundly matters.

5. Luther, WA 40/III, 343

Deus non est causa sicut causae creatae.
“God is not a cause as created causes are causes.”

Thus God cannot be modeled extensionally.

Explicatio

1. Why extensional identity is inadequate

Extensional identity holds when two expressions apply to precisely the same set of objects. If two predicates pick out exactly the same individuals, classical extensional logic treats them as equivalent. For example, if every creature that is forgiven is also elected, and every creature that is elected is also justified, then these predicates are extensionally equivalent: they have the same extension.

Formally, if for all x, x is forgiven ↔ x is elected and x is elected ↔ x is justified, then the predicates forgiven, elected, and justified are coextensive.

Similarly, in the Spirit’s work, if for all x, x speaks in the Spirit ↔ x has been given the Spirit, and x has been given the Spirit ↔ the Spirit dwells in x, then Spirit-speaking, Spirit-giving, and Spirit-indwelling are extensionally equivalent expressions.

But extensional equivalence tells us nothing about what distinguishes these divine actions in God Himself. Forgiving is not the same divine act as electing, nor is electing the same divine act as justifying. Likewise, the Spirit’s giving, indwelling, and speaking are not identical divine operations simply because they coincide in the believer. Extensional identity collapses formally distinct divine works into a single undifferentiated outcome and therefore cannot serve as the framework for a theology that seeks to speak truthfully of God’s own acting because it identifies divine acts only under the aspect of creaturely reception.

2. Why modal equivalence is insufficient

A second temptation is to appeal to modal identity. Accordingly, if two acts occur in every possible world in which God acts toward creatures, or if one cannot conceive God performing one without the other, then they are treated as identical.

Creation and preservation offer a clear example. Classical theology holds that God’s preserving of the creature is nothing other than the continued giving of being. Because no creature could exist for a moment apart from God’s sustaining act, creation and preservation are necessarily coextensive: wherever one occurs, the other is already taking place.

So too with incarnation and redemption. In the Christian confession, the Son becomes incarnate for our salvation, and His incarnate life is unintelligible apart from His redeeming work. One cannot separate them modally, for in every possible description of God’s salvific activity, incarnation and redemption occur together.

Yet modal inseparability does not entail formal identity. Creation and preservation differ in their reason, because one brings being into existence, while the other maintains that being in existence. Incarnation and redemption differ likewise, for one is the assumption of human nature, the other is the reconciling act performed in that nature. Modal equivalence cannot register these distinctions because it treats any necessarily co-occurring acts as identical, thereby losing the finer structure of God’s activity that theology must retain.

3. Why divine acts require hyperintensional individuation

If theology is to speak truthfully, it must be able to say why this particular divine act grounds this theological statement. In our broader account, a theological utterance is true because the Logos performs a determinate act—Λ ⊨* Tₜ. But determinate truth requires determinate action. If divine acts could not be distinguished except by their extensions or modal profiles, then the truthmaker for any theological statement would be some undifferentiated divine activity, and doctrinal distinctions would lose their ontological grounding.

By hyperintensional identity I mean that divine acts differ not by their outcomes or by their modal placement but by their internal form in the Logos—the determinate way God is acting here and not otherwise. This internal form cannot be captured by appeal to effects, extensions, or modal profiles; it belongs to the act as God performs it. Forgiving is formally distinct from electing because each expresses a different aspect of the divine life, even when the same creature receives both. The Spirit’s indwelling is formally distinct from the Spirit’s giving because each arises from a different manner of divine self-communication. Hyperintensionality preserves the integrity of these differences.

4. The Spirit’s donation is hyperintensional

The Spirit does not donate to creatures a general divine presence or a generic divine favor. Instead, the Spirit donates the specific act that God is performing toward the believer. In one moment, this may be forgiveness; in another, consolation; in another, empowerment. The specificity of the Spirit’s donation presupposes a finely articulated structure of divine action in God Himself. Without this specificity, divine presence would become conceptual rather than real, and theology would lose the concreteness of God’s address.

5. Felicity is indexed to particular divine acts

A theological assertion is felicitous only if it corresponds to the act God is performing here and now because that act is already determinate in God prior to its authorization in speech, already individuated in God with a hyperintensional precision. The Spirit authorizes not theological grammar in general but this particular word because this particular divine act is being given. Thus the intelligibility of theology depends on a hyperintensional account of divine acting.

Objectiones

Ob I: According to classical extensionalism if two divine acts produce the same effects, they are the same act. If this is so, there is o need for hyperintensional identity.

Ob II: Modal realism holds that if God necessarily performs A and B, then He performs A and B in all possible worlds, and thus A = B. Therefore, modal equivalence suffices in individuation.

Ob III: Thomism claims that since God is simple, all divine actions are identical and distinctions collapse.

Ob IV: Deflationism asserts that hyperintensionality describes linguistic distinction, not metaphysical difference.

Ob V: Postliberalism holds that since all distinctions arise from use within the community, divine action adds nothing.

Responsiones

Ad I: Effects underdetermine cause. Divine acts differ in their formal ratio, not merely in outcome (Gregory of Nyssa). Thus, extension collapses personal identity.

Ad II: Possible-world semantics assumes shared structure with creaturely action. But divine acts exist outside modal ontology; they ground modality rather than inhabit it. God is not a node in a modal structure but its creator.

Ad III: While implicity entails no composition in God, it does not follow that divine acts lack distinct formal identities. The Fathers held simplicity alongside real distinctions of operation.

Ad IV: Hyperintensionality is not linguistic fineness but metaphysical precision. Divine act identity is not a function of language but of participation in the Logos.

Ad V: While usage explains how we talk, it does not identify what God does. Without hyperintensional divine action, grammar loses its anchor in reality.

Nota

Hyperintensionality is the ontological form of God’s personal action. We have seen that constitutive causation (L) requires fine-grained identity; that real presence (LI) is specific, not generic; that donation (LII) concerns a particular res, and that felicity (LIII) authorizes a particular act of creaturely speech. If theological semantics were simply extensional or modal, the Trinity collapses into one role, the sacrament collapses into symbol, revelation collapses into a proposition, grace collapses into an effect, and Christology collapses into monism.

Regarding the Trinity, hyperintensionality preserves the distinction of the trinitarian persons, Christ’s unique acts, sacramental specificity, and the performative depth of divine truth. Simply put, hyperintensionality is not an analytic embellishment but a theological necessity. Without it, we could not preserve the conviction that God acts personally and decisively for the creature, nor could we maintain the integrity of the Gospel’s claim that God’s work is addressed to us in its fullness and specificity.

Determinatio

We have determined that:

1. Divine acts are intrinsically hyperintensional, distinct in their internal form even when extensionally identical.

2. Neither extensional equivalence nor modal necessity suffices to individuate divine action.

3. Hyperintensional identity flows from the Logos’ constitutive act (L) and is made present (LI), donated (LII), and authorized (LIII).

4. Theological truth (Λ ⊨* Tₜ) requires such hyperintensional grounding.

5. Therefore, theology must employ a hyperintensional semantics to speak truly of God.

Transitus ad Disputationem LV: De Intentione Divina et Identitate Actuum in Deo

Having established hyperintensionality in divine action, we proceed to the related question as to how divine intentions are related to divine acts, and how the Logos unifies them without collapsing distinctions. 

Thus, we turn to Disputatio LV: De Intentione Divina: Utrum Intentiones Dei Sint Actus et Quomodo Unitas in Logō Constituitur, where we shall inquire as to whether God’s intentions are identical with His acts, and how the Logos grounds their unity and distinction.