There are four internal divine relations in the Holy Trinity, of which only three are really distinct relations. To grasp this very important concept in the theology of the Triune God, we begin by considering again what we have said of the Trinitarian processions, namely, that there are two processions, generation and spiration. We may schematize the processions thus:
Father -> Son (Generation)
Father and Son (as one principle) -> Holy Ghost (Spiration)
The processions, in establishing distinct termini a quo and termini ad quem, give us four relations: two of origination and two of procession. For “Where there is a real procession the principle and the term are really related.” The relations may be thus diagrammed:
Father -> Son (Paternity – a relation of origination)
Father <- Son (Filiation – a relation of procession)
Father and Son-> Holy Ghost (Active Spiration – a relation of origination)
Father and Son <- Holy Ghost (Passive Spiration – a relation of procession)
Although the doctrine of the relations was developed in all its refinement by the Latin Scholastics and later defined at the Council of Florence (contra the Greek dissidents), the essential dogmatic foundation is found in the Greek Fathers. Thus, St. Gregory of Nyssa wrote, against the Eunomian objection that consubstantiality renders any distinction between the persons impossible: “Though we hold that the nature [in the Three Persons] is not different, we do not deny the difference arising in regard of the source and that which proceeds from the source; but in this alone do we admit that one Person differs from another.”
The Aristotelian definition of relation which St. Thomas borrows is “order of one thing to another [ad aliquid].” In Aristotle’s metaphysics, relation is one of the nine categories of accident. Through a process of affirmation (the via eminentia seu excellentiae) and negation (via negativa seu negationis), we can strip relation it of its character as accident so as to apply the notion to God. For, as St. Thomas affirms, “whatever has an accidental existence in creatures, when considered as transferred to God, has a substantial existence; for there is no accident in God; since all in Him is His essence.” Elsewhere, he had already negated the notion of accident: “Relationship is not predicated of God according to its proper and formal meaning, that is to say, in so far as its proper meaning denotes comparison to that in which relation is inherent, but only as denoting regard to another.”
The Dominican Doctor will go on to show that the relations are contained as distinct hypostases in God’s own essence.
Even as an accident, a relation is not primarily something inhering in a thing, but is, rather, an ordering to something outside the hypostasis itself: “But relation in its own proper meaning signifies only what refers to another [again, ad aliquid].” And elsewhere: “But the true idea of relation is not taken from its respect to that in which it is, but from its respect to something outside.”
This unique, ad aliquid, attribute of relation makes its elevation to the category of substance all the easier. Thus, it is “more than a perfection in the subject, [but] is a reference to the terminus, and its essential characteristic lies precisely in that reference (esse ad), while its inherence in the subject (esse in) is secondary, and may be real or only logical.”
Having explained the general idea of relation and affirmed its valid application to God, we will now break the concept down into its notional parts and apply this to the Persons of the Trinity. “In every real relation there are three elements: 1) the subject (father), 2) the term (son), 3) the foundation of the relation (activity of generating). [What is here said of generation can be said of the three other relations as well, mutatis mutandis.] The essence of the relation consists in being ordered to another; in Latin this is called ‘esse ad’ and the foundation [ – the reason for which the subject has reference to the term – ] is called ‘esse in.'”
Since relation is this ordering to another, it is, in our experience, between two substances (e.g., I am related to my father as his son). However, in God, the relations are between the subsistences, or hypostases, which are also known as the Trinitarian Persons. They are, then, acts ad intra, i.e., internal activities in the One Substance of the Godhead. For this reason, we call them “internal relations.”
For our intellects, limited by temporal notions of before and after, it is all too easy to conceive of the Trinitarian processions happening first; and then, once the Three Persons exist, the relations come into being. Besides the obvious objection that the processions are eternal and that God (the Most Pure Act) does not “become,” the metaphysics of this view of the processions and relations is really backwards. For, although the relations can be logically inferred immediately from the doctrine of the processions, ontologically it is the relations which constitute multiplicity in God. Thus, St. Thomas cites Boethius to the effect that “in God the substance contains the unity; and relation multiplies the Trinity.” More authoritatively, the Council of Florence defined that in God “everything is one where there is no distinction by relative opposition.” Now, the “relative opposition” is the relation.
St. Thomas lucidly explains why such a relative opposition must be posited: “The very nature of relative opposition includes distinction. Hence, there must be real distinction in God, not, indeed, according to that which is absolute, namely, essence, wherein there is supreme unity and simplicity – but according to that which is relative.” In other words, we cannot distinguish persons at all without such (metaphysical) opposition.
The relations do not merely exist between the Persons. They are the Persons, for they are subsistent relations. Thus, St. Thomas says that “relation… enters into the notion of the person…” and cites Boethius’ affirmation that “every word that refers to the persons signifies relation.” Therefore, “The fatherhood constitutes the Person of the Father, the sonship constitutes the Person of the Son, and the passive spiration constitutes the Person of the Holy Spirit.” Because these relations actually subsist, St. Thomas has it that “each divine Person is a subsistent, incommunicable, internal divine relation.” This means that when we say “Father,” we are naming a personal relation. So, too, when we say “Son,” and “Holy Spirit.”
An even stronger way of saying this is that Paternity, Sonship, and (Passive) Spiration are the three divine Persons.
The saintly author of the Summa resumes the thoughts of the previous paragraphs in the following terse language: “Therefore person in any nature signifies what is distinct in that nature… Now distinction in God is only by relation of origin…, while relation in God is not as an accident in a subject, but is the divine essence itself; and so it is subsistent, for the divine essence subsists. … Therefore, a divine person signifies a relation as subsisting. And this is to signify relation by way of substance, and as such a relation is a hypostasis subsisting in the divine nature…”
Now the question begs to be asked, “if there are four relations, why are there only three Persons?”
The answer is implicit in the Florentine definition that “everything is one where there is no distinction by relative opposition.” The active spiration (which opposes passive spiration) is not a personal (or subsistent) relation because the one Spirator is actually two Persons, namely, the Father and Son, who, “as one principle,” spirate the Holy Ghost. In other words, active spiration is identical with paternity and filiation. Said another way, the complete concept of both paternity and filiation contain in themselves the notion of active spiration, with this difference, that in paternity, spiration is from the Father Himself, whereas, in filiation, it is received from the Father.
In the words of Father Baker: “Of the four real internal divine relations, three stand in opposition to one another and, therefore, are really distinct, i.e., fatherhood, sonship and passive spiration (= Holy Spirit). The active spiration stands in opposition to the passive spiration only; it is not opposed to fatherhood and sonship and, therefore, is not really distinct from them. So there are only three really distinct relations in God which constitute the three Persons.”
St. Thomas explains this in the Summa: “Although there are four relations in God, one of them, spiration, is not separated from the person of the Father and of the Son, but belongs to both; thus, although it is a relation, it is not called a property, because it does not belong to only one person; nor is it a personal relation – i.e., constituting a person. The three relations – paternity, filiation, and procession – are called personal properties, constituting as it were the persons; for paternity is the person of the Father, filiation is the person of the Son, procession [passive spiration] is the person of the Holy Ghost proceeding.”
St. Thomas Aquinas, Summa Theologiae, Translated by the Fathers of the English Dominican Province. Online Edition: Kevin Knight, 2003. Online, available at: http://www.newadvent.org/summa/ [accessed 12 July 2006].
Parente, Pietro; Piolanti, Antonio; and Garofalo, Salvatore, Dictionary of Dogmatic Theology. Translated by Emmanuel Doronzo, O.M.I., S.T.D., Ph.D. Milwaukee: The Bruce Publishing Company, 1951.
Joyce, G. H., “The Blessed Trinity” in The Catholic Encyclopedia. Robert Appleton Company, 1907. Online Edition by K. Knight, 2003. Online, available from: http://www.newadvent.org/cathen/15047a.htm [accessed 13 July 2006].
Pohle, Rt. Rev. Msgr. Joseph, Ph.D., D.D. The Divine Trinity. Adapted and edited by Arthur Preuss. St. Louis: B. Herder Book Company, 1925.
 G. H. Joyce, “The Blessed Trinity” in The Catholic Encyclopedia (Robert Appleton Company, 1907; Online Edition, 2003 by K. Knight). Online, available at: http://www.newadvent.org/cathen/15047a.htm [accessed 13 July 2006].
 It is imperative that the Son be included in the active spiration. Filiation and and passive spiration do not establish a relative opposition between the Son and the Holy Ghost, and without the relative opposion between active and passive spiration, there is no basis for a distinction between the Person of the Son and the Person of the Holy Ghost. This is one of the many reasons why anti-filioque heresy of the Greek schismatics is so inimical to Trinitarian theology.
 Joyce, op. cit.
 Summa Theologiae Ia Q. 28, A. 2.
 Ibid., A. 1.
 Summa Theologiae Ia Q. 28, A. 2.
 Parente, Pietro; Piolanti, Antonio; and Garofalo, Salvatore, Dictionary of Dogmatic Theology, translated by Emmanuel Doronzo, O.M.I., S.T.D., Ph.D. (Milwaukee: The Bruce Publishing Company, 1951) p. 239.
 Summa Theologiae Ia Q. 28, A. 3.
 Denzinger 703. This dogma, first articulated by St. Anselm (On the Procession of the Holy Spirit), is called by Father Pohle, “The Fundamental Law of the Trinity.”
 Summa Theologiae Ia Q. 28, A. 3.
 With this in mind, what I said in footnote 2 (regarding the Son’s participation in active spiration) should be considered to see its true importance.
 Summa Theologiae Ia Q. 29, A. 4.
 Of all the notes contained in St. Thomas’ definition, the word incommunicable is not elsewhere explained in this paper. I shall do so here: Incommunicable is the inability to be communicated. Now, the Father communicates to the Son all that the Father Himself is – except the personal property of innascibility (being “not born” or being the “Origin without origin”). So, too, the Father and the Son communicate all they are to the Holy Ghost, except the Father’s innascibility and the Son’s passive generation (his being the Son). Although it may seem unnecessary because of the very notion of relation (with is, essentially, a “relative opposition”), what St. Thomas has done here in including the term “incommunicable” is add an important, additional barrier against modalism.
 Summa Theologiae Ia Q. 30, A. 2.