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.
Romans 11:33
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:
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Perfectio formalis: the internal coherence and felicity of the model.
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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.
Let V denote divine truth.
Perfectio formalis: the internal coherence and felicity of the model.
Adequatio transcendens: the model’s participatory orientation toward divine reality beyond all system.
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:
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Theological modeling is necessarily finite.
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Its limits signify divine transcendence, not error.
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Truth in theology is participatory and inexhaustible.
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The Spirit preserves both coherence and openness.
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The incompleteness of theology secures its realism.
Theological modeling is necessarily finite.
Its limits signify divine transcendence, not error.
Truth in theology is participatory and inexhaustible.
The Spirit preserves both coherence and openness.
The incompleteness of theology secures its realism.
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