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.

On the Theological Equivalency of East/West Trinitarin Models

Theologians are oftentimes too lax in getting clear on the types of claims they make. Take, for instance, the claim that the East and West made theologically equivalent claims about the Trinity, although they divided philosophically in their conceptuality about universals: The East assuming that a universal could be numerically one and multiply instantiatable, and the West denying this. Is it indeed true that the East and West make equivalent trinitarian claims?

Theoretical equivalency is understood differently on syntactical and semantic approaches. According to syntactical approaches, theories T1 and T2 are equivalent if they have, as their extension, the same or equivalent set of models. This syntactical approach to understanding theories and their equivalency was dominant through much of the twentieth century, and is oftentimes referred to as "the classical view" or "the received view." On this approach, a theory is a set of uninterpreted axioms in a specified formal language using a set of correspondence rules that provide a partial empirical interpretation to the theory by linking observable entities and processes to particular non-logical terms. A theory is true just in case its interpreted axioms are all true.

The semantic approach to understanding theories and their equivalency has developed over the last four decades. While syntactic approaches are interested in deducibility from axioms, semantic approaches focus upon the notion of "satisfaction." Objects which satisfy the axioms are models of those axioms. According to the semantic approach, the axioms comprise part of a theoretical definition. Whether or not such a definition is true of the world depends upon theoretical hypotheses. A theory is true just in case all of its associated hypotheses are true. In the words of F. Suppe, the semantic view "construes theories as what their formulations refer to when the formulations are given a formal (semantic) interpretation" (Suppe, The Semantic Conception of Theories and Scientific Realism, Chicago: University of Illinois Press, p. 4). This model-theoretic view identifies theories with the set of models that satisfies the theoretical laws of the theories. The models can be understood as being a pure structure: abstract entities and relations. Theories T1 and T2 are equivalent if and only if they are satisfied by sets if models M1 and M2 respectively, such that M1 and M2 are isomorphic to each other.

Applying this to the Trinitarian question, we might say that sentence "God is both one and three" is satisfied by two different sets of models, one employing a multiply instantiable universal, the other a property particular overlapping the compresent bundles of properties constituting the persons. If two separate sets of model structures satisfy the same set of Trinitarian propositions, these structures are equivalent and they are isomorphic with respect to each other.

It is ironic to find that East and West Trinitarian controversies may have been argued by people holding equivalent or almost equivalent Trinitarian views. Perhaps one is not making a different theological claim at all when "starting with the persons" or "starting with the essence." Maybe, in fact, the new social Trinitarianism is finally equivalent to older, more traditional Trinitarian positions.

Trinitarian Confusions between East and West?

Richard Cross has argued that the East and West do not really "adopt radically divergent accounts of the Trinity" (Richard Cross, "Two Models of the Trinity," HeyJ XLIII (2002) 275-294). I believe Cross is fundamentally correct, though I do have some observations.

It is often claimed that the Eastern view (following the Cappadocian Fathers) starts from the diversity of the persons and then moves to account for the unity of the essence, while the Western view (following Augustine) starts from the unity of the divine essence and then attempts to account for the diversity of the persons. Clearly, much has been made of this distinction in the secondary literature. One finds characterizations of the difference between East and West such as the following: The Thomistic tradition originating in Augustine assumes this order of logical priority: Relation, Person, and the Processions; the Cappodocian tradition understands the logical priority this way: Processions, Person, the Relations. (e.g., See Knuuttila & Saarinen, "Innertrinitarishe Theologie in der Scholastik und bei Luther, " pp. 243-264, Caritas Dei: Beitraege zum Verstaendnis Luthers und der gegenwaertigen Oekumene.) Cross argues persuasively that the difference between the Eastern and Western traditions has little to do with theology, but everything to do with different philosophical assumptions operating in the East and West. "The Eastern view does, and the Western view does not, generally accept a sense in which the divine essence is a shared universal" (275). Gregory of Nyssa, for instance, claims that the divine essence is a singular multiply-instantiatable universal; Augustine denies this.

Cross begins his analysis by giving the standard metaphysical options on universals and particulars. He first distinguishes the substrate/property view of the constitution of substance from that of a congeries of properties having what Russell called "compresence." Secondly, he distinguishes properties as particulars from properties as universals. Accordingly, if properties are particulars, then the indiscernible properties of numerically distinct substances are themselves numerically distinct. However, if properties are universals, then the indiscernible properties of numerically distinct substances are identical (and thus by Leibniz's law) the same property. If two particulars have the same shade of blue and if these shades of blue are particulars - - one shade of blue is exactly like the other - - , then the shades of blue are numerically diverse. However, if the two particulars have the same shade of blue and the shades of blue are literally the same shade, then the blue is a universal. A universal is, by definition, a property that can be a constituent in more than one substance. Particular properties, by definition, cannot be constituents in more than one substance. Accordingly, the only real metaphysical possibility for overlapping substances on a bundle theory (the view that a substance is a compresence of properties) is that there are universal properties that are ingredient in each and every compresence.

This insight is crucial for understanding the putative divergence between the Eastern and Western views. For purposes of analysis, allow 'substance', 'hypostasis' and 'person' to be used interchangeably, and futher assume that 'divine essence' is an overlapping property (a property common to the three substances), and must thus be, on the previous analyis, a universal. This divine essence is termed the 'ousia' by the East. As to the question of whether this divine essence is one simple universal property, or a bundle of such properties, Cross follows Augustine: "God however is indeed called in multiple ways great, good, wise, blessed, true and anything else that seems not to be unworthy of him; but his greatness is identical with his wisdom . . . and his goodness is identical with his wisdom and greatness, and his truth is identical with them all; and with him being blessed is not one thing, and being great or wise or true or good, or just simply being (esse), another" (Trin. 6.7.8 CCSI., I, 237).

Gregory of Nyssa clearly articulates the view that the universal divine essene (ousia) is a unviversal that is multiply instantiated in the three divine persons:

"If now of two or more who are [man] in the same way, like Paul and Silas and Timothy an account of the ousia of men is sought, one will not give on account of the ousia of Paul, another one of Silas andd again another one of Timothy; but by whatever terms the ousia of Paul is shown, these same will fit the others as well. And those are homoousioi to each other, who are described by the same fomular of being" ("Human Nature in Gregy of Nyssa: Philosophical Background and Theological Singnificance," Supplements to Vigilae Christianae, 46, p. 709, p. 70).

The universal which is the divine essence is clearly numerically singular:

"But the nature is one, united to itself and a precisely undivided unit (monas), not increased through addition, not decreased through subtraction, but being and remaining one (even if it were to appear in a multitude), undivided, continuous, perfect, and not divided by the individuals who participate in it" (Gregory, Abl. GNO, III/I, 40.24-41.7).

Cross points out, however, that Gregory's universal is not ante rem. The divine essence does not exist uninstantiated, but is rather immanent in the persons; it is that "of which" the persons are (Cross, 281). The divine essence is shared by the persons, but the divine persons as overlapping bundles of properties do not share their own personal properties.

According to Cross, the Western theologians implicitly accept the view of the shareability of the divine essence by the persons even though they explicitly criticize this position. The western theologians deny that the divine essence is a universal "in the sense of 'universal' accepted by the West, not the sense accepted by the East" (Cross, 281). Though they deny this, they accept that the essence is shared by the persons. Augustine writes:

"In the simple Trinity one is as much as three are together, and two are not more than one, and in themselves they are infinite. So they are each in each and all in each, and each in all and all in all, and all are one" (Trin. 6.10.12, CCSL, L, 243).

Over eight centuries later, Aquinas echoes Augustine:

"In God, the essence is really identical with a [viz., each] person, even though the persons are really distinct from each other" (ST 1.39.1, c).

Yet the western theologians explicitly reject Nyssa's view on universals. Quoting Augustine again:

"If essence is species, like man, and those which we call substances or persons are three, then they have the same species in common, as Abraham, Isaac, and Jacob have in common the species which is called 'man'; and if while man can be subdivided into Abraham, Isaac, and Jacob, it does not mean that one man can be subdivided into several single men - - obviously he cannot, because one man is already a single man - - then how can one essence be subdivided into three substances or persons? For if essence, like man, is a species, then one essence is like one man" (Trin. 7.6.11, CSSL, L, 236).

Augustine's criticism assumes that if the divine essence is a species, and if a species is divisible, then the divine essence is divisible. But since this cannot be so, he concludes that the divine essence is not a species. But if it is not a species, then it is not a universal at all. Cross believes that Augustine holds that a universal (species) is divisible because he assumes that Neoplatonic notion of in re universals. Neoplatonists are nominalists here; they claim that universals (species) are merely aggregates of particulars.

Although Aquinas is not a Neoplatonic nominalist, his Aristotelian realism agrees on this point: "No universal is numerically the same in the things beneath it" (Scriptum super Libros Sententiarum 1.19.4.2). Cross concludes: "Unlike the Eastern tradition, . . . the Western tradition accepts - - as a matter of philosophical fact - - that universals, even in re universals, are not such that they are numerically identical in each exemplification" (Cross, 284). Thus, while the Cappadocians assumed that all universals, not just the divine essence, "are numerically singular, and . . . the particulars are collections of such universals" the Western tradition rejected the claim of the numerical singularity of universals and the consitution of particulars from universals (ibid.). While both the East and the West claimed that the divine essence is a singular property formed by the intersection of the properties of the persons, the West disagreed with the East in claiming that this intersection could be accounted for by claiming the existence of a numerically identical universal. The divine essence as a universal in re is not logically or metaphysically prior to the persons, but dependent and posterior to the persons. Yet, this essence is something more than its instantiations in the persons; for this essence is what makes possible the identity of these persons.

To the objection that Eastern and Western views must be theologically distinct because social trinitarian views can be grounded in the former and not via the latter, Cross claims that such views actually cannot be grounded in one tradition more properly than the other. It is just not the case that the Western view adopts a Trinity of subsistent relations between persons disallowing a social trinitarian approach, and the East a theory of personal processions completely compatible with a robust social trinitarianism.

The Western notion of subsistent relations claims that the persons are individuated with respect to dyadic relations holding between the persons. These dyadic relations are not constitutive of the persons themselves; they do not inhere in things, but somehow "hang between" their relata. Aquinas writes:

"Distinction in God arieses only through relations of origin . . . But a relation in God is not like an accident inherent in a subject, but is the divine essence itself. So it is subsistent just as the divine essence is subsistent. Just as, therefore, the Godhead is God, so the divine paternity is God the Father, who is a divine person. Therefore 'divine persons' signifies a relation as subsistent" (ST 1.28.1, c).

Cross points to Augustine as the source of this view, for it was Augustine who denied that God can be a subject for accidents, and thus rejecting accidents, identifies relations as the non-inherent "things" whose distinction does not entail a distinction in substance: "What is stated relationally does not designate substance. So although begotten differs from unbegotten, it does not indicate a different substance" (Trin. 5.5.6, CCSL., I, 210). Because accidents require a substrate, and because the presence of a substrate is incompatible with simplicity, the assertion of simplicity requires a denial of accidental personal properties. However, "a divine person can include a relation without that relation thereby entailing composition" (287). Thus, for the West, the divine persons cannot be pyschological subjects, for such psychological subjects are necessarily individuated by their non-relational properties.

Cross believes that Gregory of Nyssa effectively also embraced the category of subsistent relations. In the following quote, the distinguishing features of the persons are clearly the causal relations they possess with respect to each other:

"While confessing that the nature is undifferentiated, we do not deny a distinction in causality, by which alone we seize the distinction of the one from the other: that is, by believing that one is the cuse and the other is from the cause. There is the one which depends on the first, and there is that one which is through that which depends on the first" (Abl. GNO, III/I, 55.24 - 56.6).

So, as it turns out, the East is close to a doctrine of subsistent relations, and the West assumes that the divine essence is shareable among the three persons. Accordingly, both East and West deny social trinitarian accounts which hold the three persons as distinct pyschological subjects. While Eastern and Western views are consistent with social accounts of the Trinity - - a shareable divine essence among persons clearly allows for pyschologically distinct subjects - - both reject those accounts because of the need to individuate persons on the basis of something other than the accidental (non-relational) properties of the persons (Cross, 288).

What is to be said of this analysis? Clearly Cross has clarified matters greatly. That God is one and three, does seem to entail that the divine essence can be shared by persons. The Western view, that this essence is a numerically singular property shared by the persons, is not at all incompatible with the Eastern view that this essence is a universal that, while it is immanent in the persons, is none the less numerically one and multiply instantiatable in them. If this is so, then the unity from which the West begins is just the shareable property/universal. While the West might ground their talk of personal diversity upon the ground of divine unity, the shareable property of divine unity is nontheless dependent upon the bundled properties constituting the persons. Alternately, while the East might ground their talk of divine unity upon the grounds personal distinctiveness, this unity clearly, like the West, remains dependent upon the existence of the persons.

Cross's analysis, if true, suggests that while the Eastern and Western views have their own metaphysical models, each satisfies the same set of theological propositions. If this is so, then there is no theological differences between the two.

Trinitarian Reflections

One can claim that in the late thirteenth and early fourteenth centuries two different Trinitarian traditions developed in the west. The first, grounded in the thought of Thomas Aquinas, claimed that relations themselves individuate the persons of the Trinity. On this view, the Father is the Father because he bears a particular relation to the Son. The second, developing in and through the work of Duns Scotus and others, claims an emanationalist model where origins individuate the persons of the trinity. The person of the Father is innascible, and by virtue of this innascibility, is the Father. On the first model, bare relations individuate the Trinitarian persons. According to the second model, particular monadic properties are possessed by the persons, properties, on the basis of which, relations among the persons are established.

With regard to the Son being the Word, the first view, because it is committed to individuation through bare relations, understands 'Word' metaphorically. It is because that the Son bares sonship to the Father that the Son is the Son. Word can be spoken of this Son metaphorically because the Son is "like a Word" in being an expression (issue) of the one who expresses (issues) it. On the other hand, the emanationalist view can regard 'Word' as specifying more or less the individuating property of the Second Person. Because the Second Person is Word, He is called the Son of God.

The distinction between internal and external relations may be helpful here in understanding the distinction. An external relation R holds of a with respect to b if and only if R does not change the entity which a is in relation to b. For example, I am externally related to my son because I remain exactly who and what I am genetically regardless of whether the relation of being the parent of b obtains or not. An internal relation R' holds of a with respect to b, however, if and only if R obtaining changes what a is in relation to b. For example, my son is internally related to me because his genetic material varies as a function of whether the relation 'being a son of me' holds or not. An external relation does not change the being of the one related to another; an internal relation does change the being of the one related to the other.

These categories can be helping for thinking about the indiviudation of persons within the Trinity. On the Fransican model, the Trinitarian persons are externally related with respect to 'being the Father of x' because the dyadic relation of Father to Son is grounded on the the existence of nonrelational, mondadic properties like innascability which themselves individuate the persons. According to the Dominican model, however, the persons are internally related with respect to dyadic relational properties like 'being the Father of x', for the Father could not be the person He is apart from the relation in question.

Using the language of logic, the Dominicans claim that the one called 'Father' is the one having two dyadic relations: 'being the Father of the Son' and 'being the one from whom the Spirit proceeds'. For the Fransicans, on the other hand, the one called 'Father' is the one having the nonrelational monadic quality of innascability, a property, on the basis of which, the relation of Father to Son is established. The two dyadic relations individuate the Father on the Dominican model; a single monadic property individuates the Father on the Fransican view.

Now things get difficult when trying to conceive how either account is possible without compromising the unity of the divine essence, or without denying real objective distinctiveness of the persons. For instance, if we say that there are either real relations or real intrinsic qualities in the persons, we seem to be claiming that there is a real ontological consitutent to individuation, a modus essendi, not merely modi intelligendi. But if this is so, it appears that divine simplicity, and hence the divine essence itself, is compromised. On the other hand, if we say that the Trinitarian individuaters are mere modi intelligendi, then the ontological distinctiveness of the Trinitarian persons seems to be undermined. There is one divine essence ontologically, although human beings might, from the standpoint of reason, distinguish that essence into persons. But if this is so, then the Persons seem to be due to human construction.

The third way also sometimes used in the tradition appears unworkable. It claimed a modus se habendi in which no distinction arises when comparing the personal properties to the divine essence, yet a distinction arises when comparing these properties to the properties of the other persons. Lamentably, this is a non-starter because the problem still remains: Are the individuating properties, upon which the persons are individuated, ontologically grounded or not? If yes, then divine simplicity seems difficult to sustain; if no, then divine simplicity is sustained at the expense of their being any real differences among the Trinitarian persons.

The problem of the identity in difference of the Trinitarian persons is a profound one, and it is clearly not solved either in the Dominican or Franciscan traditions.