On Intension and the Modeling of Theological Language
Intensio in theologia non est mera conceptio mentis, sed forma participationis, qua sermo fidelis participat in re ipsa de qua loquitur. Modeling theologicum est interpretatio huius intensionalis structurae intra ordinem entis, quo verbum fidei inseritur in veritatem ontologicam causatam a Spiritu.
Intension in theology is not merely a mental conception but a mode of participation by which faithful speech shares in the very reality it names. Theological modeling is the interpretation of this intensional structure within the order of being, through which the word of faith is inserted into the ontological truth caused by the Spirit.
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Thesis
The intension of theological language expresses the way in which meaning and being coinhere through participation. Modeling is the act by which these intensional forms are interpreted within ontological structures, so that theology’s speech corresponds to divine reality. Thus, intensionality grounds the realism of theology’s models: words mean what they mean because they share, analogically, in what they signify.
Locus classicus
“My word that goes out from my mouth shall not return to me empty, but shall accomplish that which I purpose.” — Isaiah 55:11
“My word that goes out from my mouth shall not return to me empty, but shall accomplish that which I purpose.” — Isaiah 55:11
Here the Word of God is not a sign that points to something absent, but a living act that accomplishes what it names. The divine Word is intensional in the highest sense: its meaning and its effect coincide. Theology’s task is to reflect this coincidence within the limits of human language.
Explicatio
In ordinary logic, intension refers to the content or concept of a term—what it signifies internally—while extension refers to the set of things to which it applies. In theology, however, intension cannot be reduced to mere conceptual content, for the meaning of divine terms arises from participation in the realities they signify.
When theology says “Deus est bonus” (“God is good”), the term bonus has an intension that differs fundamentally from its use in secular discourse. Its meaning is not abstracted from experience but given through participation in divine goodness itself. The Spirit mediates this participation, so that human predicates acquire analogical depth.
Let us represent this symbolically (and immediately explain):
Let I(p) denote the intension of a theological predicate p—its interior content as informed by participation in divine reality.
Let M(p) denote the modeling of that predicate—the interpretation of p within an ontological framework of being. The relation I(p) → M(p) expresses that theological modeling extends the meaning (intension) of language into ontology; what faith means, ontology makes real.
Hence, modeling theology is not constructing analogies externally but recognizing that the intensional life of faith’s language already participates in the realities to which it refers.
Theological predicates are therefore intensional in a deeper sense than philosophical ones: their meanings are not closed concepts but open participations. Each name of God carries within it a structural reference to divine causality. To speak truly of God is to allow the intension of language to become a site of encounter, where meaning and being converge.
Objectiones
Obiectio I. Aristotle and his scholastic heirs maintain the position of Aristotelian realism, the view that the meaning of predicates is exhausted by their extension to real things. Intension adds nothing to ontology. To analyze theological predicates intensionally—as if their sense exceeded their reference—is to introduce needless abstraction. The meaning of “God is good” is simply that God instantiates goodness; no intensional layer is needed.
Obiectio II. From the standpoint of empiricist verificationalism, all meaningful statements are either empirically verifiable or analytically true. Theological predicates refer to no empirically testable properties and therefore lack cognitive meaning. Model-theoretic “interpretation” of such terms merely disguises their non-referential status under formal symbols. To construct intensional models for theology is to rationalize what is semantically empty.
Obiectio III. Following later Wittgenstein, meaning arises from use within a linguistic form of life (Lebensform). To model theological language formally or intensionally is to misunderstand its grammar. The meaning of “grace,” “sin,” or “Spirit” lies in their practical employment within worship and life, not in their reference to divine properties or in hypothetical models. Modeling theology as if it described an external reality mistakes liturgical use for scientific representation.
Obiectio IV. Contemporary analytic semantics often treats meaning extensionally, defining reference via truth conditions over possible worlds. Since divine reality is not empirically accessible or multiply realizable across worlds, theological language cannot admit of model-theoretic interpretation without violating the principle of extensional adequacy. Theology should confine itself to moral or metaphorical discourse rather than claim intensional reference to the divine.
Obiectio V. George Lindbeck’s cultural-linguistic model asserts that theological statements are true insofar as they cohere with the community’s grammar. There is no external domain into which they must be modeled. To introduce an intensional semantics for theology is to reintroduce representational realism and to confuse the performative, intra-ecclesial truth of faith with philosophical speculation.
Responsiones
Ad I. Aristotelian realism rightly grounds meaning in real being but overlooks the form of participation by which finite predicates relate to divine reality. In theology, predication is not univocal: “God is good” does not signify an extensionally shared property but an analogical relation between divine perfection and finite concept. Intensional analysis captures this formal relation—it models the way predicates point beyond their finite instantiations toward infinite fulfillment. Thus, intensional semantics safeguards the analogia fidei: a structure of participation rather than mere attribution.
Ad II. Empiricist verificationism confuses empirical access with cognitive meaning. Theological terms are cognitively meaningful within the ontology of participation: they refer not by sense-data but by divine causality. Model-theoretic interpretation supplies the formal correlate of this claim. It shows that theological language can be given structured domains and interpretation functions consistent with its own rules of felicity. Intensional models do not disguise emptiness; they make explicit the structure of theological reference within divine reality.
Ad III. Wittgenstein’s insight that meaning depends on use is valid at the pragmatic level but incomplete. Theological use is itself grounded in divine authorization. The Spirit makes the Church’s grammar not merely functional but truth-bearing. Modeling theology intensionally does not deny use; it articulates the inner logic by which use participates in divine meaning. The grammar of faith is a finite surface of an infinite semantics. Without such modeling, theology remains descriptively sociological rather than truth-apt.
Ad IV. Extensional semantics suffices for empirical domains but not for theological ones, where reference involves hyperintensional distinctions between formally equivalent but ontologically distinct predicates (e.g., “Creator” and “Redeemer”). Theology must operate at the intensional level because divine properties relate analogically, not extensionally. Model-theoretic analysis extends semantics beyond possible worlds to the domain of divine possibility, the space of God’s communicative acts. Hence, intensional modeling is not optional but necessary for theology’s realism.
Ad V. Post-liberal coherence captures the communal form of theology but lacks the means to account for its truth. Theological language does not merely describe communal life; it claims participation in divine reality. Model-theoretic interpretation provides a way to express that claim rigorously. By mapping the formal language of theology (T) into an ontological domain structured by participation, it unites communal felicity (FT) with divine truth-conditions (TC). Intensionality here serves realism: it formalizes the link between faith’s grammar and God’s being.
Nota
Intensionality in theology reveals the deep correspondence between divine and human discourse. Just as the Word of God contains within itself both meaning and being—significatio et effectus—so theological speech, animated by the Spirit, partakes in that same structure.
In model-theoretic terms, theological language is not a static set of propositions but a living model in which predicates participate in the realities they denote. When theology says “Christ is Lord,” this is not a metaphor to be verified externally; it is a confession whose intension already shares in Christ’s lordship through the Spirit.
Modeling thus performs a theological epistemology of incarnation: finite words filled with infinite content, formal structure suffused with divine causality. In this sense, modeling does not invent theology’s truth but explicates it—it unfolds the internal participation already latent in theological meaning.
Hence, to study theology’s intension is to trace how language itself becomes sacramental: a sign whose signification and grace coincide.
Determinatio
From the foregoing it is determined that:
Intension in theology signifies participation: the inward meaning of a theological term is its share in divine reality.
Modeling interprets these intensional forms within an ontological framework, revealing how language and being correspond through the Spirit.
The Spirit is the cause of this correspondence, uniting signification (intensio) and reality (veritas) without confusion.
Theological precision arises not from limiting meaning but from its right participation in the divine.
Therefore, the intension of theology’s language is itself a locus of revelation: the Word that makes meaning also makes being, and modeling is the act by which this unity is rendered intelligible.