Disputatio XIII: De Intensione et Modeling Linguae Theologicae

On Intension and the Modeling of Theological Language

Quaeritur

Utrum intensio in theologia non sit mera conceptio mentis, sed forma participationis, qua sermo fidelis participat in ipsa re de qua loquitur; et utrum modeling theologicum sit interpretatio huius intensionalis structurae intra ordinem entis, per quam verbum fidei inseritur in veritatem ontologicam a Spiritu causatam.

Whether 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; and whether 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.

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

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:

1. Intension in theology signifies participation: the inward meaning of a theological term is its share in divine reality.

2. Modeling interprets these intensional forms within an ontological framework, revealing how language and being correspond through the Spirit.

3. The Spirit is the cause of this correspondence, uniting signification (intensio) and reality (veritas) without confusion.

4. Theological precision arises not from limiting meaning but from its right participation in the divine.

5. 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.

Transitus ad Disputationem XIV: De intensione et Intentione in Discurso Theologico

In considering the intension of theological language, we discerned that the meaning of theological terms cannot be exhausted by conceptual modeling. Their adequacy arises not only from logical structure but from participation in divine self-disclosure. Yet meaning, to be fully theological, must not only signify rightly but also intend rightly, that is, it must move from formal content to living reference, from concept to act.

For theology is not an inventory of divine predicates but a directed discourse of faith. What it says and how it says are bound together in the intention of the believer speaking within the Spirit. To model the divine truth is one thing; to intend that truth in the act of confession is another. Here, the intellect and the will converge in a single movement of participation: understanding becomes invocation.

Hence we advance to Disputatio XIV: De Intensione et Intentione in Discurso Theologico, where it is asked how the inner content (intensio) of theological concepts relates to the directedness (intentio) of theological speech, and whether true theology consists not in correct modeling alone but in that Spirit-led act in which language, will, and divine reality are gathered into one.

Disputatio II: De Theologia ut Systemate Modelorum

On Theology as a System of Models

Quaeritur

Utrum theologia, ut veritatem habeat, interpretanda sit intra systema modelorum, quibus expressiones syntacticae linguae fidei referuntur ad statum rerum a Deo constitutum; ita ut veritas theologica non sit mera congruentia signorum, sed consonantia inter linguam divinitus datam et esse divinitus productum.

Whether theology, in order to bear truth, must be interpreted within a system of models through which the syntactical expressions of faith’s language are related to states of affairs constituted by God; such that theological truth is not mere congruence of signs but the harmony between divinely given language and divinely created being.

Thesis

Theology, once established as a coherent formal language T, becomes truth-bearing only when its expressions are interpreted within models—structured accounts of reality that specify what exists and how what exists stands in relation to God. Modeling joins theology’s syntactical order to ontological reference and shows how speech about God corresponds to being as given by God.

Locus classicus

1. Scriptura Sacra — Psalm 32(33):6 (LXX)

Ἐν λόγῳ Κυρίου οἱ οὐρανοὶ ἐστερεώθησαν,

καὶ τῷ πνεύματι τοῦ στόματος αὐτοῦ πᾶσα ἡ δύναμις αὐτῶν.

"By the Word of the Lord the heavens were made, and by the breath of his mouth all their host."

Here divine speech and divine constitution coincide. Creation is the world shaped by a speaking God.

2. Scriptura Sacra — John 1:1–3 (NA28)

Ἐν ἀρχῇ ἦν ὁ Λόγος… πάντα δι’ αὐτοῦ ἐγένετο, καὶ χωρὶς αὐτοῦ ἐγένετο οὐδὲ ἕν.

"In the beginning was the Word… all things came to be through Him, and without Him not one thing came to be."

The Logos is not only divine speech but the personal ground of all existence.

3. Athanasius — Contra Gentes 40.2

Ἐκ τοῦ Λόγου καὶ τῆς Σοφίας ἡ σύστασις τῶν ὄντων ἐγένετο·

ὁ γὰρ Λόγος τοῦ Θεοῦ ἐποίησεν τὰ πάντα.

"From the Word and Wisdom came the constitution of beings; for it was the Word of God who made all things."

Athanasius insists that creation bears the rational imprint of the eternal Logos.

4. Augustine — De Trinitate VI.10.12

In Verbo Dei sunt rationes omnium creaturarum.

"In the Word of God are the reasons of all creatures."

Creation’s intelligibility derives from the inner intelligibility of the divine Word.

5. Thomas Aquinas — Summa contra Gentiles II.24

Quod in Deo est ratio omnium, hoc in rebus est veritas omnium.

"What in God is the reason of all things, that in creatures is the truth of all things."

Aquinas expresses the same principle: the world’s truth is participation in God’s inner reason.

These witnesses affirm a single truth: Verbum et esse unum sunt in Deo.

The Word and being coincide in God, and theology models truth only by retracing this coincidence.

Explicatio

If Disputatio I showed that theology must first be grammatically coherent, Disputatio II shows that coherence alone does not yield truth. A language of faith, no matter how precisely ordered, remains incomplete until it is interpreted within an ontological environment. Syntax without reference is empty form.

In logic, a model assigns meanings to expressions so that sentences may be said to be true or false. In theology, a model is not merely a semantic device but a structured description of the world as it stands before God. Let T denote the language of faith and M the model that depicts the divine order of creation, redemption, and consummation. To interpret T in M is to connect theological expressions to the realities that God has constituted.

For example, the confession “Christ is risen” is modeled not by symbolic reformulation but by the ontological affirmation that the crucified Jesus truly lives, an event located within God’s causally ordered world. Modeling theology is therefore not speculation added to confession but the faithful translation of divine acts into the grammar of being. It enables theology to say not only what is believed but what is.

Objectiones

Ob I. Kant limits theoretical knowledge to phenomena shaped by human categories. To model theology in relation to divine reality exceeds possible knowledge and reinstates pre-critical metaphysics.

Ob II. Heidegger argues that ontological structures conceal Being and reduce God to a highest being. To model God within being risks onto-theology and suppresses divine mystery.

Ob III. Logical empiricism insists that only empirically verifiable claims or tautologies have meaning. Theological models are unverifiable and thus cognitively meaningless.

Ob IV. Post-liberal theology maintains that religious meaning arises solely from communal grammar. Modeling introduces an external reference foreign to theology’s intratextual logic.

Ob V. Process thinkers hold that divine–world relations are dynamic and evolving. Static models distort the relational becoming of God and world.

Responsiones

Ad I. Kant’s boundary concerns epistemic access, not ontological structure. Revelation transcends these limits by grounding knowledge in divine communication. Modeling does not violate the Critique but extends it analogically: it interprets faith’s language within the world constituted by God’s Word. The Spirit mediates where pure reason cannot.

Ad II. Heidegger rightly warns against reducing God to a being among beings. Yet Christian confession does not speak of a highest entity but of the Word through whom all being is constituted. Modeling does not capture God within being but depicts being as participation in God’s creative utterance.

Ad III. Verificationism collapses under its own criterion, which is itself unverifiable. Theological models are verifiable within theology’s own domain, where truth is pneumatic rather than empirical. Their adequacy is tested by coherence with revelation and by the Spirit’s witness in the Church.

Ad IV. Post-liberal grammar rightly highlights communal practice but risks enclosure. Scripture and creed speak not only about communal life but about divine reality. Modeling makes explicit the ontological reference implicit in Christian confession.

Ad V. Process thought recognizes genuine relationality but mistakes relation for mutability. Theological models can articulate relation without surrendering divine immutability. They describe the world’s participation in God’s eternal act, not God’s evolution.

Nota

Modeling is the bridge between theology’s formal order and its truth. If FT denotes theology’s felicity conditions, then modeling furnishes its truth conditions, TC. The formula is simple:

FT + Modeling = TC.

The Spirit who authorizes theological language also mediates its rightful interpretation within reality. Modeling is not an imposition upon faith but a clarification of faith’s inherent realism. It permits theology to speak with intellectual rigor while preserving its confessional depth.

A theological model is not a cage for divine mystery but the intelligible space where divine truth becomes shareable. Through models the Church’s speech becomes not only meaningful but true.

Determinatio

1. Theological language T is incomplete until it is interpreted within models that reflect divine reality.

2. Modeling joins the syntax of faith to the ontology of creation, grounding reference in God’s act of speaking.

3. The Holy Spirit mediates both the felicity of T and the adequacy of its interpretation.

4. The plurality of models reflects the richness of divine truth refracted through creation.

5. Theology’s coherence and its truth converge where divine language meets divinely ordered being.

Thus theology becomes truth-bearing only where the Word that speaks is joined to the world that answers.

Transitus ad Disputationem III: De Spiritu Sancto et Finitudine Felicitatis

The second disputation has shown that theological truth emerges where the grammar of faith meets the structure of reality. Yet correspondence, though necessary, is not sufficient for the fullness of truth. For truth in theology is never merely structural. It is participatory. It depends not only on language and ontology but on the divine act that unites them in the life of the creature.

Theological models describe how the Word’s intelligibility is refracted into the order of creation, but they cannot themselves actualize the unity they depict. The bond between sign and reality must be effected by the Spirit, who brings coherence to completion through a living union. Without the Spirit, theological truth remains static; with the Spirit, it becomes event, communion, and joy.

Thus arises the next inquiry: how does the Holy Spirit mediate the correspondence between divine Word and created understanding? How does the Spirit transform finite cognition into participation in divine truth? These questions lead us to Disputatio III: De Spiritu Sancto et Finitudine Felicitatis.

Model-Theoretic Semantics and Theology

All too often we unthinkingly assume a "magical" view of language.   We naturally suppose that our language is anchored to the world correctly, as if our language intends to link to the world in a particular way.  For instance, we might believe that 'dog' uniquely refers to that class of which the canine at my heels is a member, and 'laptop' to that class of which this object upon which I type is an element.

However, reflection about the nature of such intentionality does not support these prima facie intuitions.    'Dog' cannot and does not intend the canine at my feet, though through appropriate human context and practice it may refer to that animal.   'Laptop' is conventionally linked to the object upon which I type these words, though it may not have been the case.

Hilary Putnam famously advanced the "model-theoretic argument against realism."  In it he purports to show that that an entire linguistic system considered as a totality cannot by itself determinately refer.   Representations, no matter how involved, are not agents and thus have no power to intend objects in the world.  Language, considered formally and syntacticly, does not in itself have meaning and cannot thus refer to the world.  Any attempt to give language such an intentionality through the use of model-theoretic semantics must fail.  In order to understand what Putnam is saying and its relevance for theology, we must understand what model-theoretic semantics is.

Model theory provides an interpretation to formal systems.  For the various symbols of a language, it assigns an extension, i.e., particular individuals, sets, functions and relations.  Model theory recognizes that since language does not magically intend objects in the world, the elements of language can only map to structures of objects.  Simply put,  given a particular function f, and any non-logical term p, f(p) graphs to a unique object in the world o.  In other words, there is a transformation from language to its extensional interpretation, a correspondence that is itself conventional.   Accordingly, while a particular function f1 maps 'dog' to the class of objects of which the canine at my feet is a member, another function f2 maps 'dog' to the last horse standing at Custer's last stand.  When we think language magically picks out the elements of the world, we simply forget that many other functional images of our language are possible.  Simply put, we forget that our language can sustain a large number of multivalent interpretations.

Model-theoretic semantics proceeds by constructing models which satisfy classes of statements, that jointly makes true those statements.   Take, for instance, this class C of statements:  'The cat is on the mat', 'John understands that an equivalence relation is reflexive', and 'All mats are owned by John'.   A model is an extensional interpretation I making all members of C true.  This might happen when 'cat' refers to the set of all domesticated felines, 'mat' to the set of all objects upon which one wipes one's feet, 'on' to a two place predicate Oxy specifying the set of all ordered pairs {x, y} such that x is adjacent and above y, 'John' to a particular person,  'understands' to a dyadic predicate Uxy forming the set of all ordered pairs {x, y} such that the first is an epistemic agent and y is that which is understood, 'equivalence relation is reflexive' to a member of the set of all concepts, and 'owned by' to a two place relation Wxy forming the set of all {x, y} such that x possesses y.  In addition, 'the cat' is a definite description uniquely picking out some member of the set of all domesticate felines, while 'the mat' uniquely refers to one member of the class of all objects upon which one wipes one's feet.  

The reader should reflect upon how difficult it is to provide an adequate intensional characterization of the set of mats or the set of things understood.   Fortunately, we don't have to pick all the properties that each and every member of the set has.  We can simply refer to the set whose members have these properties as well as others.  It is obvious that the three propositions above are true (or "satisfied") if there exists the sets in question and the members of these sets are related in the ways above specified. Let us call this interpretation I.  

Now notice that we can form I2 as follows:  Allow 'cat' to refer to the set of positive integers and 'mat' to refer to the set of negative integers, and "on to" (Oxy) to be the set of all ordered pairs {x, y} such that x is greater than y.   'The cat' now refers to a definite positive integer and 'the mat' to a particular negative integer.   Let 'John' refer to the positive integer 17 and 'understands' be the two place relation forming the set of all x such that x is the square root of y.   Assume that 'equivalence relation is reflexive' refers to 289, itself a member of the set of all odd numbers.  Finally, allow 'owned by' to refer to be the set of ordered pairs {x, y} in W, such that either x is greater than y v x=y v x is less than y.  While this interpretation may seem very artificial, it does in fact "satisfy" each member of C.  The point is that all sentences of C are true both on models I1 and I2.  

Model-Theoretic semantics provides abstract models satisfying classes of statements.  These models are sets obeying set-theoretic operations.  Clearly, we can think of the satisfaction of the classes of statements to be mappings from the constituents of those statements to unique set-theoretic structures; the relationship of the linguistic entities to their extensions are unique functions.  Each interpretation is a function from the linguistic to the set-theoretic because the following uniqueness condition holds where x is the linguistic and y the set-theoretic:  If and are members of f, then y = z. 

Putnam's argument purports to show that simply having a model that makes a class of statements true does not in and of itself determine reference.   There are an infinite number of models with different extensions that make the class of statements true!  Neither does representational similarity between the linguistic symbols and their extensions nor truth itself vouchsafe a unique reference for a language.

One way to grasp this is to consider Quine's gavagai example.   The anthropologist sees the native saying 'gavagai whenever presented with a rabbit.   But the anthropologist is sophisticated in his reflections and realizes that the native could mean 'undetached rabbit part' or 'rabbit event' or 'temporal rabbit stage'.   The model would seemingly be satisfied by any of these interpretations.   Language does not determine reference.

Putnam finds in the Lowenheim-Skolem theorem significant results which extend this insight.   The theorem holds that any satisfiable system -- that is, any system that has a model -- has a countable finite or infinite number of models.  Putnam generalizes the results of this theorem, showing that even in a system vast enough to incorporate all of our empirical knowledge, it would nonetheless be the case that there would be great numbers of models (and associated ontologies) satisfying all of the constraints of the system's theoretical and operational constraints.

While there is debate about whether Putnam's proof in "Model's and Reality" (see Realism and Reason, Cambridge: Cambridge University Press, 1983, pp. 1-25) commits a mathematical error, the general point is clear enough to anyone who has every taught an introductory logic course: Truth is always truth under an interpretation.   Agreeing on language does not an agreement make.   Agreement is only had if there exists agreement of language and a common interpretation or model.   Only if the same model is specified and there is agreement in truth-value among the relevant propositions can one speak of actual agreement.  

It should be obvious to anyone who reads theology that theological traditions have not always been clear about the interpretation of their language.   This becomes deeply clear in interfaith dialogues when two sides may use the same language, but mean something quite different with that language.   It happened, in my opinion, in the Evangelical Lutheran Church's adoption of three important documents between 1997-99:  Call to Common Agreement, the Formula of Agreement, and the Joint Declaration on the Doctrine of Justification.  The frustrating thing about those debates was that many of the participants either did not know that they needed to clarify the models they were using, or intentionally did not deeply reflect upon their interpretations for fear of losing the historic "agreement" between the parties that the ecumenical talks were supposed to engender.  

Maybe the proclivity of participants in ecumenical dialogues not to clarify the models they are assuming stems from a general historical practice among theologians to fail to specify the interpretations they employ in their own polemics and constructive work.

Take the following three propositions and assign them extensional interpretations I1 and 2.

• T1:   God creates the universe.
• T2:   All of creation has fallen into sin. 
• T3:   Through His Son, God redeems his fallen creation.  

Let I1 be the following interpretation: 

• 'God':    That being having all positive predicates to the infinite degree
• 'Creates':  A dyadic predicate whose extension is the relation {{x, y}: x causes there to be both the material and form comprising y}
• 'Universe':  All that exists outside of diving being
• 'Creation':   All that exists outside of divine being
• 'Falls':  A dyadic predicate whose extension is the relation {{x, y}: x is creation and y is the distortion of x under the conditions of present existence}
• 'Sin':  The distortion of creation under the conditions of present existence
• 'Son":  Hypostasis bearing the divine nature sustaining the following relationships of having been begotten by the hypostasis of the Father and spirating the hypostasis of the Holy Spirit
• 'Redeems':  A triadic predicate whose extension is the relation {{x, y, z}: x causes there to be reordering of y on account of z, such that x regards y as manifesting properties characteristic of the created universe 

Many readers may take issue with the extension I gave to T1-T3.   It would be an important exercise, I think, were all who employ theological language to attempt to provide a semantics like I just attempted.   It is by no means a simple task.   It is time, I believe, for theologians not simply to take responsibility for their theological language, but also for the interpretation they give that language.

Let I2  be the following interpretation:

• 'God':   To-beness in its totality.  That which is presupposed by the notions of being a particular being, and not-being a particular being
• 'Creates':  A dyadic predicate whose extension is the relation {{x, y}: x is conceptually presupposed by the class of all existing beings}
• 'Universe':  The set of all non-divine beings
• 'Creation':  The set of all non-divine beings
• 'Falls':  A dyadic predicate whose extension is the relation {{x, y}: x is creation and y is the set of attitudes, dispositions, and existential orientations of human beings phenomenologically present to human awareness as lacking the character of original creations
• 'Sin':  The existential of human existence towards the "what is" of the past rather than the "what might be" of the future 
• 'Son':  A symbol that points to and participates in the totality of being, and is capable of communicating the power of being itself phenomenologically to human beings
• 'Redeems':  A triadic predicates whose extension is the relations {{x, y, z}: x communicates the power of being itself to human beings (y) by means of the symbol of the Son (z)}  

The perceptive reader might find a trace of Tillich in interpretation I2.   The point to realize is that I1 and I2 both make T1-T3 true.   Both models satisfy a very small class of theological propositions.   Notice it is meaningless to ask if T1-T3 are true until a model has been specified upon which to evaluate their truth.  Here as everywhere in theology, truth is always truth under an interpretation.    

Theological Semantics and the Problem of Interpretation

The sentence 'the cat is on the mat' is meaningless until it has been given an interpretation. We define a function from the sentence to objects within a domain. Standardly, we should say that 'cat' refers to {x: x is a cat}, 'mat' refers to the {x: x is a mat} and 'is on' refers to { (x, y) : x is on y} . Thus, we say that there is some member of the first set a, some member of the second set b, such that is a member of { (x, y) : x is on y}. To give an interpretation is to define a function from relevant linguistic units in the language to things in the world, such that the objects in the world form a functional image f* of the language. Thus, 'the cat is on the mat' is given by f*(cat), f*(mat), and f*(cat, mat) is a member of {(x, y) : x is on y}.

Now imagine providing such an interpretation for Trinitarian discourse. 'God is the Father', 'God is the Son', and 'God is the Holy Spirit', 'the Father generates the Son', and the Holy Spirit proceeds from the Father and the Son'. One could say that f*(Father) is a member of f*(God), f*(Son) is a member of f*(God), f*(Holy Spirit) is a member of f*(God), and that {x : x is God} has one member g. Thus f*(Father) = f*(Son) = f*(Holy Spirit) = g. 'The Father generates the Son' is thus f*(Father, Son) is a member of f*{(x, y) : x generates y}. Accordingly, 'The Holy Spirit proceeds from the Father and Son' is given by f*(Father, Holy Spirit) and f*(Son, Holy Spirit) is a member of {(x, y) : x proceeds y}. What follows, of course, is that it is a member of {(x, y) : x generates y}.

Now, taking 'G' to be "generates", we have that Ggg. Lombard and the Fourth Lateran Council reject Ggg because ascribing the reflexivity of generation to the individual g seems to deny simplicity, for there seems to be no possible world in which something can generate itself without dividing itself. (Notice how one can know oneself or think oneself without dividing oneself - - if one has intuitive, nondiscursive knowledge as has traditionally been thought to be true of God.)

Martin Luther, however, had no problem affirming the propriety of "the divine essence generates the divine essence'. When he said this, he meant that the Father generates the Son. If the Father is the divine essence, and the Son is the divine essence, and the Father generates the Son, then the divine essence generates itself, Ggg. He seems to have no problems with this because if Plato is a man, and Aristotle is a man, and Plato is a teacher of Aristotle, then it is proper to say that man is a teacher of man. Of course, the set M = {x : x is a man} is not a singleton set as is D = {x : x is God}. D has one member g, but M has billions of members.

When thinking the divine essence, one must not only subscribe to it a as a general essence, but one must claim a single instantiation, for if there was more than one instantiation, there would be a compromise of monotheism.

In order to make progress on the various claims in the late medieval period, we must be able to state clearly the ontological situation of the Trinity in the most perspicuous language we possess: first-order predicate logic with identity.