Showing posts with label model theory. Show all posts
Showing posts with label model theory. Show all posts

Wednesday, October 22, 2025

Disputatio XXII: De Confrontatione Linguarum: Theologia et Saecularitas Sermonis

On the Confrontation of Languages: Theology and the Secular Word

Quaeritur

Utrum inter linguam theologicam, quae in Verbo et Spiritu fundatur, et sermones saeculares, qui autonomiam suam vindicant, oriatur verus conflictus; et utrum theologia possit adhuc praedicare veritatem in mundo, ubi scientia, ars, et cultura sibi munus veritatis usurpaverunt.

Whether there arises a genuine conflict between theological language, grounded in the Word and the Spirit, and the secular discourses that claim their own autonomy; and whether theology can still proclaim truth in a world where science, art, and culture have each usurped for themselves the office of truth.

Thesis

The theological word, because it participates in divine truth, does not compete with secular reason but interprets its conditions. The Spirit who makes theology possible also animates all authentic acts of meaning without thereby rendering them theological. Hence, theology’s speech does not withdraw from modern languages but judges and fulfills them: it discloses that every search for truth is already a response to divine communication.

Locus classicus

“In him was life, and the life was the light of men. The light shines in the darkness, and the darkness has not overcome it.” — John 1:4–5

The verse identifies the universality of divine illumination: every act of understanding presupposes the light of the Logos. Secular discourse, even in its apparent autonomy, speaks within that light and cannot escape it. The confrontation between theology and modernity is therefore not external opposition but internal forgetfulness.

Explicatio

After the Disputationes on Word and Spirit, theology now faces its cultural horizon. Modernity has multiplied languages of truth—scientific, aesthetic, political, technological—each claiming autonomy. Yet all presuppose intelligibility, value, and communicability—conditions that theology interprets as participation in the Logos.

Theological discourse (L_t) encounters secular discourse (L_s) not as rival systems but as divergent appropriations of a shared intelligible order. Formally, we may express this as two distinct interpretive relations to the same divine ground (L_∞):

LtRπL,  LsRδL

where R_π denotes participation through grace (Spirit-mediated correspondence) and R_δ denotes derivative dependence (natural reason’s participation in the Logos).

The difference is not in the object (the divine ground of meaning) but in the mode of participation.

Theology thus does not flee from modernity’s languages; it uncovers their hidden metaphysics, their reliance upon borrowed light. Where secular language treats meaning as construct, theology confesses meaning as gift.

Objectiones

Obiectio I. Scientific Naturalists like Steven Weinberg and Richard Dawkins claim that science explains the world without recourse to divine speech. Theology’s claim to interpret meaning is obsolete; language about God adds nothing to predictive or explanatory power. The “light of the Logos” is a poetic metaphor for natural intelligibility, not its cause.

Obiectio II. Philosophical Postmodernists like Michel Foucault and Richard Rorty hold that all claims to meta-language or transcendence are expressions of power. Theology’s assertion that secular reason “borrows light” masks its own will to authority. There is no divine ground of meaning—only historical formations of discourse. The Logos is another name for the dominant narrative of Western metaphysics.

Obiectio III. Voices like Paul Tillich and Don Cupitt argue that to preserve credibility, theology must translate its symbols into existential or cultural meanings. The language of revelation should yield to human experience and creativity. To claim that secular reason still depends on divine light is nostalgic; theology must learn from, not correct, secular wisdom.

Obiectio IV. John Milbank and Radical Orthodoxy claim that secular reason is not merely derivative but inherently nihilistic and must therefore be rejected, not engaged. The Church should withdraw into its own grammar, its own nova lingua, abandoning dialogue with modernity. Engagement risks corruption of the sacred by the profane.

Responsiones

Ad I. Scientific explanation presupposes an ordered reality and a rational subject capable of truth, conditions that science cannot itself generate. Theology does not compete with explanation but discloses its ground: intelligibility itself as participation in the Logos. The Spirit’s presence in the act of reason makes knowledge possible; to call this “poetic” is to confuse causality with metaphor. The light of the Logos is the ontological precondition for all epistemic light.

Ad II. Postmodern suspicion rightly unmasks language’s entanglement with power, but theology interprets this entanglement as the distortion of participation. The Spirit, not the will to power, is the true condition of meaning. Deconstruction reveals the instability of all autonomous discourse; theology explains it: when speech forgets its source, it fragments. The Logos is not a regime of power but the gift of communicability that enables critique itself.

Ad III. Liberal translation preserves relevance at the cost of reality. Symbols derive their power from the truths they signify, not from subjective resonance. The nova lingua theologiae is indeed open to culture, but as illumination, not adaptation. The Spirit interprets human experience by orienting it toward divine meaning; theology learns from culture only by discerning in it the traces of grace.

Ad IV. Radical Orthodoxy rightly insists that theology is not founded upon secular reason, but withdrawal denies providence. The same Spirit who consecrates the Church animates the world’s search for truth. The task is not isolation but interpretation—to read secular languages as estranged offspring of the divine Word. The nova lingua must not retreat but translate, not by compromise but by conversion: making alien speech once more transparent to grace.

Nota

The confrontation between theology and secular discourse is not warfare but translation. Every language of modernity—scientific, political, artistic—bears within it a theological remainder: a hunger for meaning. The nova lingua theologiae speaks into this multiplicity not as rival ideology but as the meta-language of communion, interpreting all speech as longing for the Word.

The Spirit’s illumination is thus catholic: it extends beyond the Church’s grammar to all truthful speech, wherever reason still remembers the light.

Determinatio

From the foregoing it is determined that:

  1. The confrontation between theology and secular discourse is internal to meaning itself; secular reason unknowingly depends upon the divine Logos for its intelligibility.

  2. Theology’s new language does not abolish secular languages but reveals their participatory structure and reorders them toward truth.

  3. Scientific and cultural autonomy describe functional independence, not ontological self-sufficiency; their intelligibility remains Spirit-given.

  4. Postmodern critique and liberal accommodation each err: the first by forgetting transcendence, the second by dissolving it.

  5. Theology’s task in the contemporary horizon is interpretive and missionary—to translate the world’s fragmented languages back into participation in the eternal Word.

Thus the nova lingua theologiae stands not beside but within the world’s discourse, interpreting it to itself, until every language confesses once more that “in Him was life, and the life was the light of men.”

Transitus ad Disputationem XXIII

In the preceding disputation it was considered how the language of theology stands amid the many tongues of the age—philosophical, scientific, and political—and how, within that contest of discourses, it preserves its own mode of truth. We found that theology cannot simply translate itself into the idioms of secularity without losing its substance; yet neither can it ignore those idioms, for they articulate the world into which the divine Word has entered. Theological speech must therefore discern, within the multiplicity of languages, those structures of intelligibility through which creation itself remains open to divine address.

This discernment now presses a new question. If theology speaks within a world already patterned by scientific and rational forms of understanding, what is the foundation of those forms themselves? Are the so-called “laws of nature” merely human generalizations abstracted from experience, or do they possess a deeper ontological ground that makes the cosmos intelligible to both science and theology alike? And if such a foundation exists, does it derive from the same Logos who orders all things and sustains them in being?

Therefore we advance to Disputationem XXIII: De Fundamento Legum Naturae, in which it shall be examined whether the laws of nature arise from contingent regularity or from the divine reason imprinted in creation, and how this grounding of law reveals the world as both intelligible to reason and transparent to the creative Word.

Disputatio XXI: De Meta-Lingua Theologiae: De Communicatione Verbi et Spiritus

On the Meta-Language of Theology: On the Communication of Word and Spirit

Quaeritur

Utrum nova lingua theologiae sit ille modus loquendi, in quo sermo humanus, assumptus a Verbo et animatus a Spiritu, fit instrumentum divinae communicationis; et utrum haec lingua non substituat linguas humanas, sed eas transformet, ut participent in ipsa veritate quae loquitur—ita ut in ea infinitum non tantum se revelet sed loquatur, et finitum non tantum audiat sed respondeat.

Whether the new language of theology is that mode of speech in which human words, assumed by the Word and animated by the Spirit, become instruments of divine self-communication; and whether this language does not replace human languages but transforms them, so that they participate in the very truth that speaks—in which the infinite not only reveals itself but speaks, and the finite not only hears but answers.

Thesis

The nova lingua theologiae arises where divine Word and human speech coincide under the causality of the Spirit. It is new because its being and meaning are renewed from within by divine presence. Theology thus speaks truly only as it becomes the language of divine communication itself: the eternal Word articulated in finite discourse, the infinite made audible in the finite.

Locus classicus

“We speak, not in words taught by human wisdom, but taught by the Spirit, interpreting spiritual things to those who are spiritual.” — 1 Corinthians 2:13

Here Paul identifies a linguistic transfiguration: words remain human, yet their origin and order are divine. The Spirit teaches, and through this teaching, human speech becomes the medium of divine wisdom: a new language of theology.

Explicatio

The nova lingua theologiae is the linguistic form of participation.
In philosophy, language is typically conceived as a human system of symbols; in theology, language is the place where divine and human c
ommunicability meet. The Word (Logos) is not only the content of revelation but its grammar; the Spirit is the causality that makes human utterance bear truth.

Thus, theological language is double in form but single in act:

  • Human as finite sign and historical utterance.

  • Divine as bearer of infinite meaning.

Let L∞ denote the eternal Word, the infinite language of divine self-communication. Let Lₜ denote finite theological discourse, the language of faith and confession. Finally, let Auth(Lₜ) denote the authorization of Lₜ by the Spirit.

Then:

Theological truth obtains only if Auth(Lₜ)  (Lₜ participat L∞ per Spiritum); that is, finite discourse is true not by inclusion within the divine Word but by real participation in it, as the Spirit makes human language proportionate to divine meaning.

The nova lingua is therefore neither an abstract meta-language nor a private religious dialect. It is the site where human speech becomes transparent to divine reality, where felicity (Spirit-given authorization) and truth (correspondence with divine being) coincide.

Objectiones

Obiectio I. Kantian Transcendentalism claims that human cognition is confined to phenomena structured by the categories of understanding. Accordingly, theology can express moral faith but not divine causation in thought or speech. To claim that language participates in divine Word and Spirit mistakes moral symbolism for metaphysical participation, violating the autonomy of reason and the limits of possible experience.

Obiectio II. Barth and Brunner held that revelation is the wholly other act of God, not a linguistic system accessible to humanity. Theology may bear witness to revelation but is not itself revelation’s continuation. To speak of a new language of theology that shares in divine communication is to blur the infinite qualitative distinction between Creator and creature, turning revelation into religious expression.

Obiectio III. Wittgenstein claims that meaning arises from the use of language within a form of life (Lebensform). The felicity of theological discourse is determined by ecclesial grammar, not metaphysical causation. To posit the Spirit as the cause of meaning introduces a category mistake: causation belongs to nature, not to language. The Spirit’s “authorization” adds nothing beyond communal propriety.

Obiectio IV. Hegelian Idealism claims that the Spirit realizes itself in the dialectical unfolding of human consciousness. Accordingly, theology is not a distinct divine act but the self-expression of the Absolute within finite reason. The nova lingua theologiae is thus unnecessary because human discourse already manifests divine Spirit in its self-development. To posit transcendent causality in theology regresses to pre-critical metaphysics.

Obiectio V. George Lindbeck and Kathryn Tanner both hold that theology’s truth is intralinguistic, that it is a coherent discourse within the Church’s rule of faith. Divine causation is thus a superfluous hypothesis. To claim that the Spirit determines what counts as true speech reintroduces metaphysical realism under the guise of pneumatology. The “new language” of theology should be understood as communal practice, not ontological participation.

Responsiones

Ad I. Kant’s limits define the autonomy of reason, not the transcendence of God. Revelation does not violate the categories of thought but constitutes their ground. The Spirit does not add a second cause to cognition but founds its capacity for meaning. Thus, the nova lingua arises precisely where reason is fulfilled by grace; the Spirit elevates the finite intellect to participation without abolishing its structure. Theological discourse thus becomes rational in a higher sense. a rationality transfigured by participation.

Ad II. Barth rightly insists on divine freedom, yet divine freedom includes the liberty to dwell within human language. The nova lingua does not erase the Creator–creature distinction but actualizes it: God’s Word remains transcendent even while speaking immanently. The Spirit’s presence ensures that theology is not revelation itself but its living continuation, for the Word still speaks in the Church’s speech.

Ad III. Wittgenstein’s insight that meaning arises from use is incomplete. The ecclesial Lebensform exists because the Spirit sustains it. The grammar of faith is not self-originating; it is founded in divine authorization. The Spirit’s causality is not physical but constitutive; it makes the correspondence between sign and referent possible. Without the Spirit, theology reduces to linguistic anthropology; with the Spirit, grammar becomes sacrament: the finite sign that mediates infinite truth.

Ad IV. Hegel’s dialectic rightly perceives the relation between thought and being but confuses participation with identity. The divine Word does not evolve into human consciousness; it speaks through it. The Spirit is not the world’s self-realization but God’s personal presence within the finite. The nova lingua therefore represents not the self-consciousness of reason but the descent of divine communication. Communion arises not by dialectical necessity but by grace.

Ad V. Post-liberal theology correctly locates truth within the Church’s language but cannot explain why that language bears truth at all. Felicity requires truth conditions that obtain beyond grammar, and this occurs through the Spirit’s causality. While the Word guarantees referential content, the Spirit vouchsafes participation. Thus, theology’s “new language” is not another dialect but the transformation of language itself into the site of divine truth.

Nota

To speak of the nova lingua theologiae is to confess that all true theology is God’s own discourse in the mode of the finite. The Holy Spirit determines inclusion within T (the formal language of theology) and mediates the causal link between felicity and truth. The Word provides the ontological content of that truth; the Spirit provides its efficacious form.

Hence:

FT + TC = Veritas Theologicawhere FT (felicity conditions) ensure internal coherence and authorization, and TC (truth conditions) denote the real divine states of affairs modeled ontologically by T.

The Spirit, as both formal and causal principle, unites these two in a single act of divine communication.

Determinatio

From the foregoing it is determined that:

  1. The nova lingua theologiae is the linguistic manifestation of the act of Word and Spirit: the infinite Word speaking through finite words.

  2. The Spirit’s causality is non-competitive and constitutive; it authorizes human speech to bear divine truth.

  3. The Word’s eternity is the meta-language within which all finite theological languages (Lₙ) are interpreted and fulfilled.

  4. Theological truth arises when felicity (Spirit-given authorization) is linked to truth through modeling.

  5. The nova lingua theologiae is incarnational: the infinite speaks within the finite, and the finite becomes transparent to the infinite.

In this union, theology ceases to be speech about God and becomes God’s own speech through the creature, language redeemed into truth, and truth made audible as the living Word.

Transitus ad Disputationem XXII

The preceding disputation disclosed that the meta-language of theology is not a neutral system above divine speech, but the living communicatio between the Word and the Spirit, the eternal dialogue through which divine truth both descends into and gathers up finite discourse. Within this communication, the human theologian speaks only insofar as the Spirit appropriates human language into the self-expression of the divine Word. Theology is thus dialogical in its very essence: it exists as participation in an ongoing conversation between God and the world.

Yet every divine conversation meets a worldly reply. The Word that enters human speech inevitably encounters other languages—philosophical, scientific, political, and poetic—each claiming its own authority over meaning. How does theology, as the speech of the Spirit, engage these rival discourses without losing its distinctive mode of truth? Can the language of faith coexist, translate, or contend with the languages of secularity, or must it reclaim a logic of its own, irreducible to the grammar of the age?

Therefore we proceed to Disputationem XXII: De Confrontatione Linguarum: Theologia et Saecularitas Sermonis, wherein it shall be examined how the sacred and secular orders of speech meet and resist one another, how theology maintains its truth within the pluralism of tongues, and how the Spirit sustains the integrity of divine discourse amid the babel of the world.

Tuesday, October 21, 2025

Disputatio XIX: De Meta-Lingua Theologiae et Verbo Divino

On the Meta-Language of Theology and the Divine Word

Quaeritur

Utrum meta-lingua theologiae non sit sermo humanus aliis superior, sed ipsum Verbum divinum, in quo et per quem omnis lingua creata interpretatur; et utrum Deus non habeat aliud verbum de se quam se ipsum, ita ut Logos sit meta-lingua analogice dicta, qua universa loquela humana in veritatem redigitur.

Whether the meta-language of theology is not a human discourse standing above others but the divine Word Himself, in whom and through whom all created language is interpreted; and whether God possesses no other word about Himself than Himself, such that the Logos is the meta-language, analogically so called, by which all human speech is gathered into truth.

Thesis

The only true meta-language of theology is the eternal Word. All human theological languages—old, new, symbolic, propositional—exist as finite object-languages within the field of divine communication. The Logos is both their ground and their interpreter, the infinite discourse in which their partial meanings are united and fulfilled.

Locus Classicus

“In the beginning was the Word, and the Word was with God, and the Word was God.” — John 1:1

This verse establishes the primacy of divine speech: before there were languages, there was the Word; before there were signs, there was meaning itself. The divine Logos precedes, grounds, and interprets every act of human speaking. The Word is not one being among others but the intelligible act by which all that is becomes intelligible.

“Tu autem eras interior intimo meo et superior summo meo.”
“But You were more inward than my inmost self and higher than my highest.”Augustine of Hippo, Confessiones III.6.11

Augustine here confesses that God is not encountered as an object within language or consciousness, nor as a voice external to the soul, but as the interior ground of intelligibility itself. God is nearer than thought and prior to every act of understanding. This inwardness is not subjectivity but ontological priority: the Logos as that by which both mind and meaning are possible.

Taken together, these witnesses establish that the Word of God is not merely spoken to creatures but spoken in them, not as a linguistic artifact but as the living source of sense and truth. The Logos is thus rightly confessed as theology’s true meta-language: not a discourse about God, but God’s own self-articulation in which all created speech finds its meaning and measure.

Explicatio

The notion of meta-language in logic and model theory designates a higher-level language used to describe the rules, syntax, or semantics of another. In theology, such a separation is impossible. No language can stand outside the Word of God in order to describe it, for all language already exists within the act of divine self-communication. All human discourse remains within the domain of divine utterance, because the Word is both the Creator of speech and its ultimate hearer. This meta-lingua is not transcendental consciousness nor a meta-subject interpreting meaning, but the very ratio intelligibilitatis of being and speech.

Thus, when theology speaks about God, it does so within God’s own communicative act. The Logos is not an external commentary on the world but the internal ratio by which it exists and becomes intelligible. Every language—whether philosophical, poetic, or dogmatic—functions as an object-language within the comprehensive “meta-language” that is God’s eternal self-utterance.

This means that the relation between divine Word and human language is not hierarchical but participatory, that is, a relation of constitutive causality in the order of signification. Let us represent this formally (and then explain it):

Let L₁, L₂, L₃ … denote the many object-languages of creation: ordinary speech, philosophical reasoning, scriptural idiom, the nova lingua of faith.

Let L∞ denote the divine Logos, the Word that encompasses and grounds all finite discourse.

Then for every Lₙ, the relation Lₙ ⊂ L∞ holds analogically. This symbol of inclusion does not name a merely logical or set-theoretic relation, but signifies ontological dependence: each finite language exists and is intelligible only through the constitutive causality of the Word. This is not linguistic hierarchy but participation grounded in Logos.

Hence, divine meta-language is not an external code but the infinite ontological horizon of interpretation which precedes and grounds every act of understanding. The Spirit mediates this participation, translating the divine Word into the polyphonic tongues of creation and returning creation’s words into praise.

Objectiones

Obiectio I. Ludwig Wittgenstein and the later linguistic turn argue that language-games possess internal criteria of meaning; there is no meta-language beyond them. To claim that the Logos functions as a meta-language imposes a totalizing framework that violates the autonomy of forms of life.

Obiectio II. Karl Barth maintains that revelation is wholly event and never a stable linguistic form; thus, there can be no divine meta-language, for God’s Word encounters us only as momentary address, never as standing structure of meaning.

Obiectio III. Jacques Derrida and his heirs hold that all language is differential play without final referent or transcendental signified. The claim that the Logos interprets all language reintroduces a metaphysics of presence which deconstruction has exposed as illusion.

Responsiones

Ad I. Wittgenstein rightly observes that meaning arises within language-games at the level of human use. Theology, however, concerns the ground of linguistic possibility itself. The Logos is not a competing game but the fundus of all grammars, the ratio loquendi that makes any signification possible. Without the Word as ontological ground, even internal coherence loses intelligibility.

Ad II. Barth rightly emphasizes the event-character of revelation, but the event itself presupposes the eternal Word. The Logos is not a static structure but the living continuity of divine speech. Revelation as event is the historical manifestation of that eternal discourse. Thus, divine meta-language is not a standing text but the ongoing act of self-communication through the Spirit.

Ad III. Deconstruction’s critique of presence inadvertently confirms the theological claim: no finite language can secure its own meaning. The Logos, however, is not an available presence within language but the transcendent act that bestows meaning upon the play of difference. The Spirit does not close différance but transfigures it into relation.

Nota

To speak of the divine Word as theology’s meta-language is to confess that all truth is linguistic because all being is spoken—not as linguistic construction, but as Logos-grounded intelligibility. The cosmos itself is a sentence within the discourse of the Logos. In this sense, theology’s many models and expressions, as examined in Disputationes XVII–XVIII, are not rival statements but varied declensions of a single Word.

This view transforms the philosophy of language into a theology of communion. Meaning no longer rests upon formal conventions or social contracts but upon participation in the divine speech-act that sustains creation. Hence, all interpretation is ultimately Christological: every word finds its coherence only in the Word made flesh.

Formally we may write (and then explain):

∀w ∈ Lₙ, Meaning(w) = Participation(w, L∞),

where this participation grounds both reference (Refₘ) and the donation of theological sense (Ref*ₗ). Semantic realism thus appears as the linguistic echo of creation’s metaphysical realism.

The Church, as communio verbi, is the living medium of this divine meta-language in history. Its confession, liturgy, and doctrine are not human projections upon silence but Spirit-authorized articulations of the eternal discourse of the Word and Spirit. In the Church’s speech, divine meta-language enters temporal form without loss of transcendence.

Determinatio

From the foregoing it is determined that:

  1. The divine Logos is the only true meta-language of theology: the eternal act of meaning in which all created languages participate.

  2. All human theological discourse (Lₙ) functions as finite object-language within this horizon; its truth lies in participation, not autonomy.

  3. The Spirit mediates this participation, translating the eternal Word into temporal speech and returning human language into praise.

  4. Philosophical denials of meta-language rightly expose the limits of human systems but fail to see that divine discourse is not a system but the very act of meaning itself.

Therefore, theology’s meta-language is not analytical but incarnational: the Word made flesh is the hermeneutical center in which all human words are gathered and made true.

Transitus ad Disputationem XX

The preceding disputation has shown that theology cannot transcend itself by means of a higher, detached language. Its meta-lingua is not an external code but the reflexivity of the divine Word within finite speech: the Word illumining itself in the medium of human discourse. Theology thus appears not as commentary upon revelation but as revelation’s own self-interpretation, the finite word drawn into the infinite articulation of God’s Logos.

Yet this discovery opens a deeper question. If theology truly occurs within the self-speaking of the Word, what is its mode of actuality? How does the human act of theologizing participate in the divine act of speaking? What role belongs to the Spirit, through whom finite utterance is gathered into the living voice of God?

Therefore we advance to Disputatio XX: De Theologia ut Actu Verbi et Spiritus, in which theology will be considered not as a superior human discourse about the divine, but as the very action of the Word and Spirit—an event wherein God, in speaking through human language, continues the eternal dialogue of truth within time.

Monday, October 20, 2025

Disputatio XVIII: De Finibus Modeling Theologici et Transcendentia Veritatis; Prooemium ad Partem III: De Logica et Incompletudine;

Prooemium ad Partem III: De Logica et Incompletudine

Why Theology Must Confront the Limits of Reason

The theological inquiry now turns from language to logic, from signification to formal necessity. Having examined how divine truth becomes speakable in human discourse, theology must now ask how that same truth encounters the structures of reason itself, and where reason, in fidelity to its own vocation, must acknowledge what exceeds it.

Logic stands at theology’s threshold. It promises rigor, necessity, and demonstrative clarity. Yet every attempt to formalize truth also exposes the limits of formalization. The human intellect, in seeking to order intelligibility into complete systems, discovers that any consistent system of finite propositions is necessarily open: truths arise that cannot be derived within the system that recognizes them. This discovery, rendered precise in Gödel’s incompleteness theorems, is not a defeat of reason but its purification. It reveals that reason’s strength lies not in closure but in its capacity to witness beyond itself.

Throughout the history of thought, the aspiration toward a total logic has repeatedly reappeared. Aristotle sought closure through syllogistic necessity; the medievals through scientia demonstrativa; Descartes through clarity and distinctness; Leibniz through the characteristica universalis; the positivists through symbolic formalism. Yet each attempt, by pressing logic toward completeness, has uncovered the same structural paradox: the more consistent the system, the less it can account for its own truth. Theology receives this paradox not as contradiction but as confession: finite reason mirrors the infinite Logos precisely in its inability to ground itself.

Within the model-theoretic vision of these Disputationes, logical incompleteness is interpreted as the formal analogue of the creature’s dependence upon God. Just as every theory requires a model in which its sentences are true, so every act of reasoning presupposes a reality that transcends its formulations. Truth exceeds provability; intelligibility exceeds syntax. The Infinite is the necessary truth-ground of the finite. Thus logic is not alien to theology but already oriented toward it. The law of thought itself bears witness to the Logos who is both Reason and Revelation.

Praefatio ad Partem III: De Logica et Incompletudine

On the Limits of Theological Modeling and the Transcendence of Truth

Ratio concludit, et revelatur infinitum

Theology speaks because truth gives itself to be spoken. Yet what gives itself is never given exhaustively. Divine truth is not an object that can be captured within finite form, but the living intelligibility in which all forms participate without containment.

For this reason, theological models are always provisional, not because they are arbitrary, but because they are faithful. Their finitude is not a defect but a sign of transcendence. Where modeling reaches its boundary, theology does not fall silent from ignorance, but pauses in reverence.

This praefatio therefore frames the inquiry that follows. If truth is participatory and grounded in the Logos, then transcendence is not opposed to intelligibility. It is its depth. The limits of language do not negate truth; they testify to its excess.

The task of theology at this point is not to abandon speech, but to learn how speech fails well: how it gestures beyond itself, how it allows silence to speak, and how it confesses truth precisely where conceptual mastery ends.


Disputatio XVIII: De Finibus Modeling Theologici et Transcendentia Veritatis

On the Limits of Theological Modeling and the Transcendence of Truth

Quaeritur

Utrum omne modelum theologicum sit verum participative sed finitum formaliter; et utrum hic finis non sit defectus sed indicium transcendenciae veritatis divinae, quae non comprehenditur sed communicatur; ac demum utrum Spiritus Sanctus hunc ordinem servet, ut finitum maneat capax infiniti sine confusione.

Whether every theological model is true by participation yet finite in form; and whether this limit is not a defect but a sign of the transcendence of divine truth, which cannot be comprehended but can be communicated; and finally, whether the Holy Spirit preserves this order so that the finite remains capable of the infinite without confusion.

Thesis

Theological models are necessarily bounded expressions of divine truth. Their formal incompleteness is not failure but fidelity. Each model bears witness to a truth that exceeds it, and this excess is the very condition of theological realism. Divine transcendence is not what theology fails to reach, but what it faithfully signifies precisely by not exhausting.

Locus Classicus

“O altitudo divitiarum sapientiae et scientiae Dei! Quam incomprehensibilia sunt iudicia eius, et investigabiles viae eius.”
Romans 11:33

The Apostle confesses not ignorance but excess. Divine truth is known truly yet never comprehensively. Theology does not abolish mystery; it articulates it.

Explicatio

Every theological model interprets the language of faith (T) within an ontological structure that renders its claims intelligible. Yet such interpretation is intrinsically finite. No model can coincide with divine truth, for divine truth is not a formal object but the living ground of all intelligibility.

This finitude is not accidental. It belongs to the structure of modeling itself. Theological models inhabit teleo-spaces of intelligibility grounded in the Logos. These spaces draw finite forms toward meaning without permitting enclosure. To model truly is therefore to articulate within an order that precedes the model and exceeds it.

Formally:

Let M denote a theological model.
Let V denote divine truth.

The relation

M ⊂ V

does not signify containment of truth within the model, but participation of the model within truth. The inclusion is analogical, not spatial. Divine truth exceeds every formal articulation because it is grounded in God’s self-being, not in conceptual determination.

This limit does not undermine theology. It secures it. If theology could exhaust divine truth, God would be reduced to a logical totality. Instead, the Spirit preserves an open horizon of intelligibility, a structured incompleteness analogous to the Gödelian insight that no consistent system can internalize the conditions of its own truth.

Thus, theological incompleteness is not epistemic failure but ontological honesty. To speak truly of God is to acknowledge that one’s speech refers beyond itself to an inexhaustible fullness of meaning.

Two horizons of truth therefore govern theological modeling:

  • Perfectio formalis: the internal coherence and felicity of the model.

  • Adequatio transcendens: the model’s participatory orientation toward divine reality beyond all system.

The Spirit mediates between these horizons, ensuring that finite models remain ordered toward the infinite without collapsing into silence or confusion.

Objectiones

Ob I. If every theological model is limited, theology can never yield certainty.

Ob II. Limits imply unknowability, collapsing theology into apophatic negation.

Ob III. Gödelian incompleteness introduces an alien mathematical formalism into theology.

Responsiones

Ad I. Theological certainty is not exhaustive comprehension but participatory assurance. Certitudo fidei rests on communion with the faithful God, not on formal closure.

Ad II. Limits do not negate knowledge but sanctify it. Cataphatic and apophatic speech are concentric movements around the same truth. To know God truly is to know Him as inexhaustible.

Ad III. The Gödelian analogy is not foundational but illuminative. It  clarifies a structural truth: intelligibility exceeds formalization. Logic witnesses this excess; theology names its ground.

Nota

The finitude of theological models reveals their vocation. They are not idols but icons. An idol contains what it names. An icon reveals what exceeds it.

Theological models are icons of truth: finite forms rendered transparent to infinite meaning. The Spirit ensures their porosity, guarding them from closure while sustaining their coherence.

Hence theology’s structure is eschatological. Every true model anticipates fulfillment beyond itself, when formal adequacy and divine presence will finally coincide, not by exhaustion but by glorification.

Symbolically:

T + M → V*

where V* denotes transcendent truth as the ground of all participation. The notation reminds us that truth always exceeds its representations even as it grants them reality.

Determinatio

From the foregoing it is determined that:

  1. Theological modeling is necessarily finite.

  2. Its limits signify divine transcendence, not error.

  3. Truth in theology is participatory and inexhaustible.

  4. The Spirit preserves both coherence and openness.

  5. The incompleteness of theology secures its realism.

Transitus ad Disputationem XIX

The limits of modeling reveal that theology speaks within two orders at once: the human order of finite signification and the divine order of self-communicating truth. Every theological utterance, if true, participates in both. It speaks of God while being spoken by God.

This double belonging presses the inquiry forward. If theology’s words are grounded in divine intelligibility, then what is the nature of that grounding? Is there a meta-linguistic horizon in which theological discourse is authorized and unified? And how does this horizon relate to the eternal Logos in whom all meaning is already articulated?

We therefore proceed to Disputatio XIX: De Meta-Lingua Theologiae et Verbo Divino.


Disputatio XVII: De Modeling et Veritate Theologica

On Modeling and Theological Truth

Quaeritur

Utrum modeling theologicum sit actus interpretationis, quo lingua fidei T per Spiritum in ordine entis interpretatur et inhabitat, ut veritas divina in forma creata manifestetur; et utrum veritas theologica non sit mera correspondentia, sed participatio, ita ut modelum fiat locus in quo significatio finita communicat cum veritate infinita.

Whether theological modeling is the act of interpretation by which the language of faith T, through the Spirit, is interpreted within and inhabits the order of being, so that divine truth is manifested in created form; and whether theological truth is not mere correspondence but participation, such that the model becomes the site where finite meaning communicates with infinite truth.

Thesis

Modeling in theology mediates between the formal structure of faith’s language and the reality of divine being. It is the Spirit’s interpretive act by which finite expressions are rendered adequate to divine truth. Thus, theological truth arises when the language of faith is modeled within ontological participation—when speech and being converge under the causality of the Spirit.

Locus classicus

“Sanctifica eos in veritate; verbum tuum veritas est.”
John 17:17

Christ does not identify truth with correct description but with the Word itself. Divine truth is not represented by language from without but participated from within. Theological modeling therefore does not construct truth but aligns finite speech to the truth that precedes and grounds it.

Explicatio

The term modeling in theology designates the act of relating T, the formal language of faith, to its referent in divine reality.
Earlier disputationes established that:

  • T (Disputationes I–V) is syntactical and governed by felicity,

  • divine causality (VI–VII) ensures the real participation of creaturely being in God, and

  • divine intentionality (X–XVI) grounds meaning and language in God’s own communicative act.

Modeling now unites these strands. 

Modeling does not create the ontological environment in which theology speaks. That environment is already given. Language is intelligible because it inhabits teleo-spaces of meaning grounded in the Logos as objective intelligibility. Theological modeling therefore does not insert discourse into being but articulates finite forms within an intelligible order that precedes all interpretation. The Spirit’s work is not ontological fabrication but faithful alignment: rendering finite models transparent to the Logos that lures intelligibility into form.

To model theology is not to construct analogies from below but to interpret forms drawn from revelation within the teleo-spaces of participation that make meaning possible. Every theological model is a finite schema through which divine truth becomes intelligible without being exhausted

Formally (and then explained):

  • Let T = the language of faith.

  • Let M = the ontological model interpreting T.

  • Let FT = the felicity conditions under which speech is rightly ordered.

  • Let TC = the truth conditions under which that speech corresponds to being.

The structural relation:

FT + M → TC means that when faith’s language is interpreted within a Spirit-formed ontological model, its felicity becomes truth. In simpler terms: theological modeling is the Spirit’s way of making language true.

This makes theology’s truth participatory rather than merely propositional. A model does not “mirror” God as a copy but “shares” in God as a participation. Its adequacy is analogical: it communicates divine truth in finite mode.

Thus, the veritas theologica is always twofold — immanent within the model and transcendent beyond it. No model contains God, yet each true model signifies and participates in God’s truth.

Objectiones

Obiectio I. According the the logical positivist tradition of Ayer and Carnap, theological models cannot, by definition, be verified or falsified by experience. They are neither analytic nor synthetic propositions but expressions of emotion or moral attitude. Modeling such language formally only disguises its non-cognitive nature. To call theological models “true” is to misuse the word “truth.”

Obiectio II. According to George Lindbeck and post-liberal theology, 
religious language functions like grammar within a community of faith. Modeling theology in reference to divine reality reintroduces an outdated representationalism. Theological statements are true when they coherently express the community’s faith, not when they correspond to an external metaphysical domain. Truth is intra-linguistic, not ontological.

Obiectio III. The analytic realism of Alston or Swineburn would likely argue that model-theoretic semantics, by abstracting theological assertions into formal systems, actually removes them from their epistemic grounding in revelation and evidence. Theology must rest on propositional revelation and rational inference, not on semantic or metaphysical models. Modeling may aid clarity but cannot determine truth.

Obiectio IV. The process and open theism of Hartshorne might object that modeling presupposes static ontology and determinate truth conditions, but God and creation exist in dynamic relation. If the divine reality itself is temporal and evolving, theological models that aim for determinate truth are conceptually obsolete. Truth in theology should be relational and open-ended, not formalized and fixed.

Obiectio V. Postmodern constructivism, e.g., Jean-François Lyotard and Mark C. Taylor argues that all models are human constructs reflecting power, history, and language. Theological “models” therefore reveal only the imagination of believers, not divine reality. There is no metalanguage of truth, only competing narratives. To speak of Spirit-grounded modeling is to mask human construction in theological authority.

Responsiones

Ad I. Logical positivism’s verification principle undermines itself, being neither analytic nor empirically verifiable. Theological models, by contrast, are truth-apt within the ontological domain established by revelation. They are not empirical hypotheses but formal articulations of divine causality and participation. Truth here is not observational but metaphysical—an adequation between language and the divine act of being. The Spirit secures this adequation by constituting reference: the link between the finite symbol and the infinite reality it signifies.

Ad II. Post-liberal coherence captures the communal form of theology but not its referential depth. The Church’s grammar is Spirit-constituted, not self-enclosed. Modeling theology does not abandon grammar; it explicates how grammatical felicity opens onto truth.
Theological statements are true not merely because the community authorizes them but because the Spirit interprets them into ontological reality. Modeling thus bridges communal coherence (felicity) and divine correspondence (truth).

Ad III. Analytic realism is correct in affirming propositional truth, but theological propositions derive their meaning from participation, not mere correspondence. Model-theoretic structure preserves formal rigor while accommodating the transcendence of its referent.
Revelation supplies the data; modeling orders it logically and ontologically. Truth in theology is not confined to human inference but extends to divine causation: the Spirit ensures that models do not merely describe revelation but participate in its act.

Ad IV. Process theology rightly emphasizes relationality, but divine relationality is not temporal becoming; it is the eternal act of self-communication. The Spirit’s causality is continuous, not evolutionary.
Theological models do not freeze divine life into static concepts; they describe stable relations of participation within the dynamic plenitude of God. Truth in theology remains determinate because God’s being is faithful—unchanging in love though living in relation.

Ad V. Postmodern constructivism exposes the finitude of all discourse, but theology interprets this finitude as the very site of divine communication. The Spirit’s presence does not negate historical contingency but transfigures it.Theological models are indeed human in form, yet divine in authorization. Their truth is pneumatic: God speaks in and through finite structures of meaning.To deny all meta-language is itself a meta-linguistic claim; theological realism acknowledges limitation without surrendering truth. The Spirit makes human language capable of transcendence.

Nota

Modeling theology is the grammar of divine realism. It allows theology to speak truthfully of God without collapsing into empiricism or fideism. Each formal model M interprets the language of faith within an ontological environment of participation, where the believer’s predicates correspond to divine correlates:

D_G → D, where D_G denotes a divine property (e.g., goodness in God) and D its participated correlate in the believer.

This relation, mediated by the Spirit, ensures that theology’s language does not float above reality but is anchored in divine causation. Hence, modeling is not speculative construction but a mode of communion: the structured correspondence of word and being within divine speech itself.

The Church, as communitas interpretans, lives within this modeling process. Its doctrine, liturgy, and confession are the Spirit’s ongoing interpretation of divine truth into the finite forms of history.
Theology’s models thus evolve not by invention but by the Spirit’s continual translation of the one Word into ever-new horizons of intelligibility.

In this sense, the entire economy of revelation can be described as a divine modeling of truth in time — the Word becoming flesh, history, and sacrament.

Determinatio

From the foregoing it is determined that:

  1. Modeling in theology is the Spirit’s act of relating faith’s language T to divine being, rendering it true through participation.

  2. Theological truth is participatory, not merely representational: the model is a locus of communion between finite meaning and infinite reality.

  3. The multiplicity of models reflects the analogical fullness of divine truth, not its relativism.

  4. The Spirit mediates all modeling, ensuring coherence between felicity (right speaking) and truth (real being).

  5. Theology thus achieves realism without idolatry: its words do not replace God but share in His communication.

Transitus ad Disputationen XVIII

Theology has discerned that its language of modeling is not a mere imitation of scientific representation, but a mode of participation in divine revelation. Through analogy and symbol, models open a window into the reality they cannot contain.Yet every model discloses its own insufficiency. To signify the infinite is always to fall short of the infinite. Therefore, the more faithfully theology speaks, the more deeply it senses the silence that surrounds its words.

Hence, modeling truth leads inevitably to the recognition of transcendence. If divine reality is the act by which all meaning is given, then no finite structure can encompass it without distortion. The limits of modeling are therefore not obstacles to truth but its boundary markers, the signs where creaturely thought acknowledges its dependence on the uncreated Light.

Thus we advance to Disputatio XVIII: De Finibus Modeling Theologici et Transcendentia Veritatis, in which we ask whether theological models can ever be adequate to divine reality, how truth manifests itself beyond conceptual form, and how the transcendent Word gathers even the failure of language into the fullness of His self-disclosure.