An Inquiry into Trinitarian Predication through the Categories of Aristotle
The Dedicatory Preface and the Problem Posed
The tractate opens with a dedication addressed to John the Deacon, whom Boethius identifies as an ecclesiastically learned interlocutor capable of following the philosophical precision the inquiry demands. Boethius presents the problem not as a matter of mere theological curiosity but as a genuine philosophical difficulty arising from the inherited grammar of Trinitarian confession. The Christian tradition had received, through the councils and through the accumulated labor of patristic theology, the affirmation that the Father, Son, and Holy Spirit are three and yet that the divinity itself is one. The question Boethius now places before John is precise and technical: when one predicates “Father,” “Son,” and “Holy Spirit” of the divinity, in what logical mode does such predication operate? Specifically, are these names predicated substantially — that is, do they refer directly to the divine substance itself — or do they operate in some other categorical register?
Boethius signals immediately that the answer cannot be left to pious intuition alone. The Trinitarian formula has generated a genuine logical puzzle. If “Father,” “Son,” and “Holy Spirit” each name the divine substance substantially, then the question arises how three substantial names can refer to only one substance without collapsing into the conclusion that three substances are being named. If they do not name the substance, then their mode of predication must be identified. The tractate is entirely devoted to resolving this problem by appealing to the Aristotelian doctrine of categories, which Boethius treats as the most reliable instrument available for disciplining theological language.
The Aristotelian Inheritance: The Ten Categories
Before turning directly to the Trinitarian question, Boethius recalls the Aristotelian classification of predication. Aristotle had organized all possible ways in which something can be said about something into ten irreducible modes: substance (ousia / substantia), quantity (quantitas), quality (qualitas), relation (ad aliquid / relatio), place (ubi), time (quando), position (situs), state (habitus), action (actio), and passion (passio). Each category names a distinct way in which a predicate can attach to a subject. Crucially for Boethius, these categories do not all function the same way when applied to God. Most of them attach to finite things with a kind of ontological weight — they genuinely add something to the thing they qualify, or they genuinely separate one thing from another. This is not the case for all categories when predicated of the divine nature.
Boethius draws particular attention to the category of substance and to the category of relation. When one predicates something substantially of a being, one is saying something that touches the very being of that thing — something that names what it is in itself. When one predicates something relationally, one is not adding to the being of the thing but is indicating how it stands with respect to something else. A man is a substance; a father is a father only in relation to a son. The predicate “father” does not name the substance of a man but his relation to another. Boethius will exploit this distinction as the key to the Trinitarian problem.
He notes, however, that in the case of God, the category of substance operates differently than in creatures. Among created things, substances are individuated and numerically distinct — there are many men, many horses, many stones. The numerical multiplication of substances in finite things follows from the fact that their being is composed of form and matter, and the same form can be received by many different parcels of matter, generating many numerically distinct individuals within the same species. God, however, is not composed of matter and form. The divine substance is simple in the most radical sense: God is not a being that has goodness, or has power, or has existence, but rather God simply is goodness, is power, is existence. There is no distinction between what God has and what God is. This means that whenever something is predicated of God substantially — whenever something is said that touches the divine essence itself — it must name the entire undivided simplicity of that essence, and cannot generate numerical plurality.
The Rule Governing Substantial Predication of God
From this account of divine simplicity, Boethius derives a formal rule that will govern the entire inquiry: whatever is predicated of God substantially is predicated of the three persons alike and without distinction. If “good” names the divine substance, then the Father is good, the Son is good, and the Holy Spirit is good — and these three are not three goods but one good, because the predicate in each case reaches the same undivided substance. Similarly, if “God” is a substantial predicate, then Father is God, Son is God, and Holy Spirit is God, yet there are not three gods but one God. The same holds for “eternal,” “omnipotent,” “creator,” and every other name that refers to what God essentially is.
This rule is not merely a conventional theological assertion. Boethius grounds it in the metaphysics of simplicity. When a predicate is substantial — when it reaches the substance of the thing — it cannot generate numerical multiplication in something whose substance is absolutely one and uncomposed. The multiplication of substantial predications of God (Father is God, Son is God, Spirit is God) therefore collapses into a single substantial reference, and the three statements are equivalent to saying “God is God” in three different grammatical approaches.
Boethius is careful to note that this is not the case among creatures. If three men are each said to be “just,” the justice in each man is a real quality that inheres in three numerically distinct substances. The three justices are genuinely three, even if they belong to the same species. Among human beings, substantial and accidental predication does produce numerical plurality, because the underlying substances are themselves numerically many. God’s absolute simplicity means that no such multiplication is possible at the level of substance.
The Problem with Applying This Rule to Trinitarian Names
The difficulty that drives the entire tractate now becomes fully visible. The Trinitarian names — Father, Son, Holy Spirit — appear to behave differently from other divine names when subjected to the rule just established. If these names are substantial, then the rule requires that they be predicated of each of the three persons alike and without distinction. But this generates manifest absurdity. If “Father” is a substantial name, then the Son would be a Father, and the Holy Spirit would be a Father, and yet orthodoxy requires that the Father alone is Father. Similarly, if “Son” names the divine substance, then the Father would be Son, which contradicts the fundamental Trinitarian grammar. And if “Holy Spirit” names the substance, then Father and Son would each be the Holy Spirit, which again collapses the distinctions that Trinitarian theology is committed to preserving.
The predications “Father,” “Son,” and “Holy Spirit” are therefore clearly not interchangeable among the persons in the way that “good,” “eternal,” and “God” are interchangeable. This shows that these names cannot be operating in the same categorical mode as genuinely substantial predicates. They must belong to a different category. And the category to which they belong, Boethius argues, is that of relation — the category of ad aliquid, of being said with reference to something else.
The Category of Relation and Its Special Logic
Boethius elaborates carefully on the nature of relational predication. A relation, in the Aristotelian scheme, does not name what a thing is in itself but how it stands with respect to something else. The same individual can be both a father (with respect to his son) and a son (with respect to his father) without any change in his substance. The relational predicates do not add to or subtract from the substance of the thing they qualify; they simply locate it within a web of references to other things.
In the case of the Trinity, Boethius proposes that “Father,” “Son,” and “Holy Spirit” function as relational predicates in precisely this sense. “Father” names the first person not in terms of what he is in himself — in terms of his substance — but in terms of his relation to the Son. “Son” names the second person not substantially but in terms of his relation to the Father from whom he is begotten. “Holy Spirit” names the third person in terms of his relation to both Father and Son, proceeding from them in a mode appropriate to the Spirit.
Because these names are relational rather than substantial, the rule governing substantial predication does not apply to them. The rule says that substantial predicates must be interchangeable among the persons. Relational predicates carry no such requirement. A relation names how one thing stands toward another, and when there are multiple distinct relations — Father to Son, Son to Father, Spirit to both — the names that express these relations will differ among the persons without this difference touching the unity of the substance.
This is the decisive move of the tractate. The Trinity is not a plurality of substances but a plurality of relations. The one divine substance subsists in three distinct modes of relation, and the names that distinguish the persons from one another are names of these relations, not names of three different substances or three different versions of the divine essence.
Relation Does Not Introduce Accidental Difference
Boethius anticipates a potential objection. The Aristotelian categories of accident include relations. If “Father” and “Son” are relational predicates, and if relations are accidents in the Aristotelian taxonomy, does this mean that the distinction between Father and Son is an accidental distinction — that is, that the persons differ from one another the way a substance differs from its accidents? This would be theologically problematic, because it would imply that the persons are modifications or attributes of the divine substance, rather than genuinely subsisting realities.
Boethius addresses this with care. He acknowledges that in created beings, relations are indeed accidents — they belong to the category of accident and are ontologically dependent on the substance they inhere in. The fatherhood of a human father is an accidental quality that comes and goes as his child is born or as he dies; it does not penetrate to the substance of the man himself. But God’s relations cannot be accidental in this sense, because God is absolutely simple and admits of no accidental modifications. If any relation were accidental in God, it would imply that God could change — that the relation could come to be or cease to be — and divine immutability excludes this.
The relations in God are therefore not accidents in the ordinary sense. They do not inhere in the divine substance as adventitious modifications. Rather, they are in some sense constitutive of the persons themselves — they are not things added to the persons but are the very mode in which the single divine substance is three persons. The relational distinctions are real, but they do not compromise the simplicity of the substance, because they do not introduce any composition or mutability into the divine being.
Boethius is working here at the frontier of what the Aristotelian categorical scheme can handle. The standard Aristotelian framework was designed for created things, in which substance and accidents are cleanly separated and relations are firmly accidental. When this framework is applied to God, the categories must be used in a modified and analogical way. Substances in God do not generate numerical plurality in the way finite substances do. Relations in God are not adventitious accidents in the way finite relations are. The categories retain their logical structure — the distinction between what is said substantially and what is said relatively — but their ontological implications are transformed by the infinite simplicity of the divine nature.
“Father,” “Son,” and “Holy Spirit” as Names of Relative Subsistence
Boethius develops the positive account of Trinitarian predication by saying that the Trinitarian names refer to relative subsistences — to the three modes in which the one divine substance subsists in relation to itself. The Father subsists as the one from whom the Son proceeds; the Son subsists as the one who proceeds from the Father; the Holy Spirit subsists as the one who proceeds from both. These are not three substances but three relational modes of the one substance’s subsistence.
The term “person” (persona), which was the inherited Latin Trinitarian vocabulary, is thus given a relational interpretation. A divine person is not an independent substance in the way that a human individual is an independent substance. A divine person is the divine substance considered in a specific relational mode — in the mode of being-from-another (the Son’s relation to the Father), or being-the-source-of-another (the Father’s relation to the Son), or being-the-joint-procession-from-two (the Spirit’s relation to Father and Son).
This relational account protects both the unity of the divine substance and the reality of the personal distinctions. The unity is protected because the relational distinctions do not introduce any partition, composition, or multiplication at the level of substance — there remains exactly one divine substance, one divine nature, one divine being. The reality of the distinctions is protected because the relations themselves are not merely conceptual or nominal — they are real features of the divine life, not merely different names we apply to the same indistinguishable reality.
The Contrast with “God,” “Good,” and “Great”
To sharpen the argument, Boethius contrasts the Trinitarian names with genuinely substantial divine names. When one says “God is great,” “greatness” is a substantial predicate — it refers to the divine substance, which is its own greatness, not a substance that participates in greatness from outside. Because “great” is substantial, the rule applies: Father is great, Son is great, Holy Spirit is great, and these three are not three greats but one great. The three statements converge on a single substantial reference.
When one says “Father is God” and “Son is God,” similarly, both statements predicate “God” substantially of the same undivided divine nature. The Father is the entirety of what God is; the Son is the entirety of what God is; and yet there are not two gods, because the predicate “God” in each case names the same one substance. The two statements do not generate two substantial referents but are two relational approaches to the one divine substance.
By contrast, when one says “the Father is the Father” and attempts to predicate “Father” of the Son as well, the predicate resists transfer. “Father” is a relational name — it names the first person in his relation to the second. To predicate “Father” of the Son would be to say that the second person stands in the same relation to the Son that the first person does, which would generate an infinite regress or would collapse the personal distinction entirely. The resistance of the Trinitarian names to interchangeable predication is itself diagnostic evidence that these names belong to the category of relation rather than substance.
Boethius also considers “same” and “equal” as relational predicates that can be applied within the Trinity. The Father is equal to the Son, the Son is equal to the Holy Spirit, and so on. These are relational assertions — they name how the persons stand in regard to one another — and they are true because the persons share identically the same divine substance. But even these relational predicates do not generate substantial multiplication. “Equal” names a relation, not a substance, and so the equality among the persons is a real feature of their relational life without implying that there are three equalities inhering in three different substances.
The Limits of Categorical Predication in Theology
Boethius pauses to note something important about the status of all categorical predication when applied to God. The ten Aristotelian categories were devised as an inventory of the modes in which things can be said about finite beings — beings that have substance, that are qualified by accidents, that exist in space and time, that act and are acted upon. God, as the absolute simplicity that underlies and transcends all creaturely being, does not fall under the categories in the same way that finite things do.
When the categories are applied to God, they are applied in a modified or transferred sense. Substance, when predicated of God, does not mean a bounded, individuated, composite being of a certain kind, as it does for creatures; it means the absolute simplicity of being itself. Relation, when predicated of God, does not mean an adventitious accident that modifies a pre-given substance; it means the internal constitution of the persons within the divine unity. Place, time, action, passion — most of the categories cannot meaningfully attach to God at all, and Boethius does not attempt to force them. He selects only those categorical distinctions — substance and relation — that can be applied to God in a disciplined and qualified way.
This is a methodologically important moment in the tractate. Boethius is not claiming that the Aristotelian apparatus maps cleanly onto divine being. He is claiming that the distinction between substantial and relational predication, when applied carefully and with the necessary theological qualifications, provides the most precise available conceptual instrument for articulating the Trinitarian mystery without falling into contradiction. The categories are tools of philosophical grammar, and as tools they can be used with greater or lesser precision; Boethius is arguing for their precise application in this domain.
The Question of “Holy Spirit” and the Procession
Boethius gives particular attention to the predicate “Holy Spirit.” While “Father” and “Son” express a bilateral relation — each defines itself in terms of the other — “Holy Spirit” names a more complex relational situation. The Spirit proceeds from both the Father and the Son (the Latin Filioque tradition, which Boethius represents). The Spirit’s relational name therefore involves a double referent: the Spirit is the Spirit of the Father and of the Son, and his personal identity within the Trinity is constituted by his procession from both.
This does not, however, mean that “Holy Spirit” is a substantial predicate. It remains relational — it names the third person in terms of how he proceeds, not in terms of a distinct substance. The complexity of the Spirit’s relations (from Father and from Son, rather than from a single source) does not violate the logic of relational predication; it simply means that the relation in question is more complex than the simple bilateral relations of Father and Son. The Spirit’s subsistence is constituted by a relation of procession from two, just as the Son’s subsistence is constituted by a relation of generation from one.
The Preservation of Divine Unity
Throughout the tractate, Boethius returns repeatedly to the central theological commitment that drives the entire analysis: the divine substance is one and absolutely simple. The relational account of Trinitarian predication is the philosophical instrument that makes it possible to maintain both this unity and the reality of the personal distinctions. If the Trinitarian names were substantial, there would be three substances — tritheism. If the Trinitarian names named nothing real — if “Father,” “Son,” and “Holy Spirit” were merely three names for the same indistinguishable reality — there would be no genuine personal distinctions — modalism or Sabellianism. The relational account steers between these two errors.
The persons are genuinely distinct because their relations are genuinely distinct. The relation of the Father to the Son is not the same as the relation of the Son to the Father — fatherhood and sonship are distinct relations, each real, each constitutive of a distinct mode of subsistence. And yet the substance that subsists in these distinct relational modes is numerically and essentially one, undivided, simple.
This is why Boethius insists that the relational distinctions among the persons do not separate (separare) the substance but merely distinguish (distinguere) the persons. Separation would imply that the one substance is divided into three portions, each possessed by a different person — a kind of partition of the divine being that would generate three diminished and partial gods. Distinction within relation involves no such partition. The entire undivided divine substance is the Father, is the Son, is the Holy Spirit — not distributed in portions but wholly present in each relational mode. The relational distinctions are internal to the divine life without fracturing the divine unity.
The Role of Logic as a Theological Tool
An important dimension of the tractate is its methodological stance on the use of logic in theology. Boethius takes it as given that the mysteries of faith are not irrational but are capable of being examined with the tools of reason, including formal logic and the categories of Aristotle. The Trinitarian formula, as received by faith, presents a specific logical structure — three persons, one substance — and it is the philosopher’s task to identify the categorical mode of predication that can accommodate this structure without contradiction.
Boethius does not present the philosophical analysis as a replacement for faith or as an independent derivation of the Trinity from first principles. The Trinitarian formula is given by Christian revelation and received by faith. What philosophical analysis can do — and what this tractate attempts — is to show that the formula is logically coherent: that there is a precise categorical mode of predication (relational rather than substantial) in terms of which “Father,” “Son,” and “Holy Spirit” can be affirmed as truly distinct without this distinction implying a plurality of substances.
This is a foundational move in what will become the scholastic tradition of rational theology (theologia rationalis). Boethius’s tractate is one of the earliest and most technically precise examples of the application of Aristotelian logic to Christian dogma, and it established a precedent — and a conceptual vocabulary — that later thinkers, from John Scotus Eriugena through Anselm and Aquinas and beyond, would take up and extend.
The Conclusion of the Tractate’s Main Argument
The central argument of the tractate reaches its conclusion through the following chain of reasoning: the Trinitarian names “Father,” “Son,” and “Holy Spirit” cannot be substantial predicates, because if they were, they would be interchangeable among the persons (since any substantial predicate of the divine essence applies equally to all three persons), and yet they are manifestly not interchangeable. Therefore they must belong to some other category. The category to which they belong is relation (ad aliquid). As relational predicates, they name the three persons in terms of the genuine and distinct relations that constitute each person’s mode of subsisting — the Father as the one who begets, the Son as the one who is begotten, the Holy Spirit as the one who proceeds. These relations are real, not merely nominal, and they genuinely distinguish the persons from one another. But because relations, as such, do not name the substance but only how a substance stands with respect to something else, these relational distinctions among the persons do not imply any distinction at the level of substance. There remains one substance, one divinity, one God — subsisting in three genuinely distinct relational modes.
The Problem of Number and Plurality
Boethius extends the argument to address a further puzzle about number and plurality in the Trinity. Ordinary numerical plurality requires that the things being counted differ from one another in some substantial way — three men differ because they are three distinct parcels of matter informed by the same form, or because they possess individually distinct forms. The number three, when applied to the persons of the Trinity, cannot involve this kind of substantial plurality. Three divine persons are not three instances of the divine nature, as three men are three instances of human nature.
The numerical language of Trinitarian theology — “three persons,” “one substance” — must therefore be understood in a transformed sense. The “three” of the persons refers to the three distinct relations, not to three distinct substances. The “one” of the substance refers to the absolutely simple and undivided divine being that subsists in all three relational modes without multiplication. Number, when applied to God, does not work the way it works in arithmetic or in the counting of finite individuals. It is applied relationally — counting the distinct modes of relation — rather than substantially — counting distinct units of being.
This is why Boethius insists that Trinitarian plurality is a plurality according to relation (pluralitas secundum relationem), not a plurality according to substance or according to any accidental modification. The same logic that governs the categorical analysis — the distinction between substantial and relational predication — also governs the interpretation of Trinitarian numerical language.
Trinitarian Predication and the Grammar of Divine Names
The final movement of the tractate concerns what might be called the grammar of divine names — the rules that govern which names can be applied to God in what ways. Boethius sketches a classification: some names apply to God substantially and are therefore predicated equally of all three persons (God, good, great, eternal, etc.); some names apply to God relatively and are predicated of individual persons in terms of their specific relations (Father, Son, Holy Spirit, and also names like Begetter, Begotten, Proceeding); some names — those that imply corporeality, location, temporal succession, mutability — cannot be meaningfully applied to God at all.
The relational names within the second class are further subdivided. Some relational names express how the persons stand with respect to one another within the Trinity (Father, Son, Holy Spirit — naming the immanent relations of origin). Others express how the divine persons stand in relation to the created order (Creator, Lord, Ruler — names that arise from the relation of God to creatures and that apply to all three persons alike as the single cause of creation). Boethius notes that this external relational predication — terms like “Lord” applied to God in relation to his creation — does not introduce any real change or composition in the divine being. The relation of God to creatures is a real relation on the side of creatures (creatures really are dependent on God) but does not add anything to or change anything in the divine substance itself.
The Persistent Mystery Within the Logical Clarity
Boethius does not claim that the logical analysis dissolves the mystery of the Trinity into a transparent and fully comprehensible proposition. The analysis shows that “Father,” “Son,” and “Holy Spirit” are relational predicates and that relational predicates, unlike substantial ones, can be genuinely distinct without implying a plurality of substances. This shows the logical coherence of the Trinitarian formula. It does not explain what the divine relations are in themselves — what it means for the divine substance to subsist in three relational modes, what the inner life of the divine Trinity consists of, or how an absolutely simple being can be genuinely three-in-relation. These remain properly theological and ultimately mysterious questions that philosophical grammar can illuminate but cannot dissolve.
The tractate functions, within Boethius’s body of work, as an application of the logical and metaphysical tools he had developed through his translations and commentaries on Aristotle’s Categories and On Interpretation and on Porphyry’s Isagoge. The theological tractates, of which this is one, represent Boethius’s attempt to show that the same Aristotelian framework that disciplines philosophical inquiry is adequate — with appropriate modification and qualification — to illuminate the logical structure of the central doctrines of Christian theology.
The Address to John and the Standards of Theological Discourse
Boethius’s dedication to John the Deacon is not merely a literary convention. It reflects a considered judgment about the appropriate audience and method for this kind of inquiry. The tractate presupposes familiarity with the Aristotelian categories, with the Trinitarian vocabulary of the councils, and with the history of Trinitarian controversy. It is addressed to someone capable of following closely argued philosophical reasoning and of testing each step against both the demands of logic and the requirements of orthodox theology.
Boethius implies that theological questions of this depth require both fides (faith, the reception of revealed doctrine) and ratio (reason, the disciplined application of logical and philosophical analysis). Neither alone is sufficient. Faith without rational discipline risks falling into the imprecision that allows heresy to take root — confusions about the mode of predication that lead to tritheism on one side or to the collapse of personal distinctions on the other. Rational analysis without faith risks pursuing logical elegance at the expense of the revealed content that gives the inquiry its subject matter. The tractate models the conjunction of both — beginning from the received Trinitarian formula and applying the sharpest available philosophical tools to its logical structure.
Predication, Substance, and Relation: The Terminological Legacy
The vocabulary that Boethius deploys in this tractate — substantia, relatio, persona, ad aliquid, praedicatio, numerus — became the standard Latin vocabulary of medieval Trinitarian theology. Boethius’s formulation that the Trinitarian names are predicated relatively rather than substantially was taken up by every subsequent Latin theologian who addressed the problem of Trinitarian predication. Thomas Aquinas, in the Summa Theologiae, would construct his treatment of the divine persons on the foundation of precisely this relational analysis, elaborating the notion of subsistent relations to account for the way in which the divine relations are at once genuinely constitutive of the persons and yet entirely identified with the divine substance rather than being accidents added to it.
The tractate also established the principle that the divine essence, considered in itself and apart from the relational distinctions of the persons, is the proper referent of all substantial divine predication and that the unity of this essence is maintained not by suppressing the personal distinctions but by locating those distinctions at the categorical level of relation rather than substance.
The Structure of the Divine Names in the Tractate’s Account
Taking the tractate’s account as a whole, the following structure emerges for the divine names. At the level of substance: names such as God, good, great, eternal, powerful, wise, just, simple, unchangeable — these are predicated of the three persons equally and of the divine essence as such. They refer to the one divine nature that is common to Father, Son, and Holy Spirit without multiplying or dividing that nature. At the level of relation within the Trinity: names such as Father, Son, Holy Spirit, Begetter, Begotten, Proceeding — these are predicated of individual persons in terms of their distinct relational modes of subsisting. They do not refer to three substances but to the three relational characters that distinguish the persons within the one divine life. At the level of relation to creation: names such as Lord, Creator, Ruler — these arise from the real dependence of creatures on God and are predicated of all three persons collectively, since the single divine cause of creation is the undivided Trinity.
The names that express spatial location, temporal occurrence, bodily form, passibility, and compositeness — ubi, quando, situs, habitus, actio in its corporeal sense, passio — are either entirely inapplicable to God or applicable only in the most attenuated and analogical manner, as when one speaks of God acting in history or dwelling in the hearts of believers, with the understanding that such language is accommodated to human comprehension rather than literally descriptive of the divine mode of being.
The Final Formulation
The tractate arrives at its definitive answer to the question posed at the outset. Father, Son, and Holy Spirit are not predicated substantially of the divinity. Substantial predicates apply to all three persons equally and without distinction, since they refer to the one divine essence that the three persons share wholly and without partition. “Father,” “Son,” and “Holy Spirit” do not apply equally to all three persons — the Son is not the Father, the Father is not the Spirit — and therefore they cannot be substantial predicates. They are predicated relatively — each name refers to the specific mode of relation in which one divine person subsists with respect to the others. These relational predicates genuinely distinguish the persons without multiplying the substance.
The divine unity is preserved by the rule that substantial predications of God do not generate numerical plurality. The divine plurality of persons is preserved by the recognition that relational predications can be genuinely distinct without introducing any division into the substance they qualify. The apparent paradox of three persons and one substance is not dissolved — it remains a mystery proper to the divine life — but it is shown to be logically articulable: there is a precise and coherent categorical account of how “Father,” “Son,” and “Holy Spirit” can be three genuinely distinct names referring to one genuinely undivided divine being.
