DRAFT OF A CHAPTER

 

THE TRINITY

Charles P. Poole, Jr.

Original version 1979; rewritten January, 2004; revised June, 2006

         

CONTENTS

 

                     1.  Introduction

                     2.  Structure in God

                     3.  Athanasian Creed

                     4.  God in Terms of Four Interaction Levels

                     5.  Person and Nature

                     6.  Internal (ad Intra) Interactions of Transcendent and Immanent God

                     7.  External (ad Extra) Interactions of God

                     8.  Strong and Weak Interactions

                     9.  Mission and Appropriation Interactions

                   10.  Dynamism of the Trinity

                   11. Traditional Explanations of the Trinity

                   12.  Recent Speculations on the Trinity

                   13.  Christian Prayer

                   14.  Irreducible Tensor Model

                   15.  Discussion

                         Appendix: Irreducible Tensor Model

 

Go to Top

1.  INTRODUCTION

 

          Belief in the Trinity has been one of the central tenets of the Christian Church  from the earliest centuries of its existence.  This is attested to by the fact that the three persons of the Blessed Trinity are mentioned in all of the creeds.  In this chapter we will give some  rationale as to why a scientist might have a special interest in the Trinity, we will discuss some of the characteristics of the Trinity, and in an appendix  we will propose a mathematical model for it. Much of the material presented here was obtained from the 1972 book The Triune God by Edmund J. Fortman S. J.

Go to Top

 

2.  STRUCTURE IN GOD

                                                         

          During the past couple of centuries scientists have been probing deeper and deeper into nature, and at particular steps in the process they keep finding more and more of what they call structure. Examining seemingly uniform solid objects at a magnification of a billion shows that they are not continuous, but rather composed of discrete atoms.  The size of the atom is determined by electron clouds which surround its tiny nucleus, a nucleus which is a million times smaller than the electron clouds.  Further probing shows that the nucleus itself is not a uniform entity, but rather that it is composed of several or many quarks.  Biologists have found that the organs of the body are composed of tissues, tissues are composed of cells, and cells themselves have a substructure.  Astronomers tell us that outer space contains many widely separated galaxies, and each galaxy is mostly empty space populated by billions of stars.  At each level of probing over various distance scales we scientists find more diverse structure.   These facts lead a scientist who believes in God to pose the question: Is there structure in God?   Only Christianity upholds the belief that there is but one God, but this one God has a triune or trinitarian variety of structure.  Since everything else has structure,  it should not be surprising that God also has structure.  Theologians down through the centuries have tried to gain some understanding of this structure through the light of revelation assisted by reason.  Toward the end of this chapter we will try to gain some small additional insights into the nature of this structure by postulating a mathematical model which seems to mimic some of its salient characteristics.

 

Go to Top

3.  ATHANASIAN CREED

 

          Neither the familiar Apostles’ Creed nor the Nicene Creed favor us with much specific  information about the Trinity, so we will begin our discussion of it by quoting from the more detailed so-called Athanasian Creed which provides what is probably the best formal statement of the doctrine from the early middle ages.  The Latin name for the Athanasian Creed is its two opening words Quicumque vult (salvus esse) meaning “Whoever wishes (to be saved).”   This Creed was not actually composed by St. Athanasius (c.295-373), but rather by a student of St. Augustine (354-430) about the year 500 AD.   

 

          The Athanasian Creed states: “The Son is from the Father alone, not made nor created, but begotten.  The Holy Spirit is from the Father and the Son, not made nor created nor begotten, but proceeding or spirating.  So there is one Father, not three fathers, one Son, not three sons, and one Holy Spirit, not three holy spirits, and in this Trinity none is before or after another, none is greater or less, but all three persons are co-eternal with one another and co-equal.  So that in all things, as has already been said above, both Unity in Trinity and Trinity in Unity are to be adored.  Therefore whoever will be saved must believe this of the Trinity.” 

 

          In this statement there is an emphasis on the Son begotten from the Father alone, and the Holy Spirit proceeding from both the Father and the Son.  The terminology "begotten" and "proceeding" differs in the two cases.  A second emphasis is on the equality of the persons, and a third emphasis is on their coeternality.  The overall statement of the creed corresponds to what we will refer to later as the immanent Trinity.  The final sentence notes that belief in the Trinity is necessary for salvation. 

 

Go to Top

4.  GOD IN TERMS OF FOUR INTERACTION LEVELS

 

          The word interaction is widely used in science to denote how two or more entities relate to, influence,  effect, or change each other.   We refer, for example, to the sun interacting with the earth through the force of gravity, and the collision of two pool balls is considered as an interaction between them.  The entity called God can be considered in terms of four levels of interaction. 1)  The first is the monotheistic God without interaction.  This is God with three as yet indistinguishable persons.  2) Next we introduce for consideration, or in the language of science we turn on, the mutual interpersonal interaction.  This provides us with a transcendent or immanent God who also exhibits internal interactions such as mutual love between three now distinguishable persons , what theologians call operationes ad intra.  3)  Third we add the world, which corresponds to adding the interactions of creating and sustaining the world in existence.  This provides us with the so-called economic God, an immanent God who also has external interactions, what theologians call operationes ad extra.  4)  Finally we add the covenant - incarnation - redemption - indwelling in souls - interactions and we obtain the familiar Christian God.   These four levels of interaction may be correlated with traditional subdivisions of treatises on dogmatic theology: 1) God (de Deo Uno), 2) The Trinity (de Deo Trino), 3) God the Creator (de Deo Creante et Elevante), and 4) God the Redeemer (de Verbo Incarnato et Redemptore).  The next few sections will discuss these factors in much more detail. 

 

Go to Top

5.  PERSON AND NATURE

 

          In order to describe the Trinity properly, and to compose an adequate expression of our beliefs, it was necessary for the Church fathers to develop an unambiguous terminology involving non-biblical words, namely:  nature or substance, and person or hypostasis.  From a simplified point of view “nature” answers the question “What is God?," and “person” answers the question “Who is God.”   The nature, substance, or essence of something is what makes it what it is, its internal unity, together with what governs its activity.  Person adds the notion rational or intellectual, capable of love; a person has dignity and individuality.  Boethius’ (c.480-524) famous definition is “a person is an individual substance of a rational nature,”  Richard of St. Victor (d. 1173) offered the definition ”an incommunicable existence of the divine essence,” and Thomas Aquinas (c.1225-1274) suggested “a relationally distinct subsistence in the divine nature.”  We say that God has a divine nature that makes God what God is, and that God consists of three rational, loving, intellectual persons.  The Father and the Holy Spirit are each persons which possess only a divine nature; and the Son is a person with both a divine nature and a human nature. 

 

Go to Top

6.  INTERNAL (AD INTRA) INTERACTIONS OF

TRANSCENDENT AND IMMANENT GOD

 

          God as monotheistic is called transcendent because He exists independent of the world.  God as triune is as described in the Athanasian Creed. This triune God is called immanent, and consists of three divine persons with an internal life of mutual interaction among themselves.  In theological terminology these mutual internal interactions are called operationes ad intra, and they are indeed basic to the essence of the Trinity.  They antedate the world, are occurring now, and will continue indefinitely.  This viewpoint is more in conformity with St. Bonaventure’s emphasis on a rather dynamic God who is pure activity, in contrast to St. Thomas Aquinas’ emphasis on a seemingly more static God who is pure act.  

 

          Traditional theology does not discuss the three divine persons in isolation in the Trinity, but as related to each other through the begetting and spiration operations. The Catechism says (#255) “The real distinction of the persons from one another resides solely in the relationships which relate them to one another.”   Some mediaeval Thomists maintained that only opposed relations like paternity and filiation distinguish the divine persons, but their interpersonal interactions also differentiate them.  Augustine considers the Holy Spirit as a bond between the Father and the Son, as their mutual gift.  Some have associated the Holy Spirit with the mutual love between the Father and the Son.  To me these two approaches seem too limiting and too specialized.  From a broader perspective the three persons are individually identified by their roles in a dynamic relationship; they have mutual roles to play in their reciprocal activities of interpersonal love. This mutual coexistence or living together is called circumincession (circumincessio), and it arises from the consubstantiality, from the origin, and from the relationships of the persons.   In actuality we know very little about these operations ad intra that we have been discussing, but theologians love to speculate about them, motivated by the Anselmian adage fidens quaerens intellectum, faith seeking understanding.    

 

          We have seen how the three relations of paternity, filiation and spiration express the distinctiveness or diversity of the three divine persons, but it is not clear to what extent, if at all, these persons are composed of, or are constituted by, these relations. 

 

Go to Top

7.  EXTERNAL (AD EXTRA) INTERACTIONS OF GOD

 

          God has external activities of interaction with the world, called operations ad extra, which are associated with the presence of God in the world.  The perspective of God interacting with the world is sometimes referred to as the economic Trinity.  Examples of operations ad extra are the creation of the world, sustaining the world in existence, the Old Testament Covenant with the Israelites, the Incarnation, the Redemption, the Covenant with individual Christians through baptism, and the inhabitation or indwelling of God in the souls of the just.  St. Augustine said that “God is everywhere by the presence of divinity, but not everywhere by the grace of inhabitation.”  

 

          There is ample evidence that in some activities of God in the world, a particular person of the Trinity plays a role that differs from those of the other two persons.  For example, Jesus Christ is truly the Second Person of the Trinity, and is also true man.  The interaction between the Godhead and the world which produced the Incarnation was an interaction which involved the Second Person in a particular and specific manner.  The Holy Spirit was involved with bringing about the virginal conception of Jesus in Mary (Catechism #485).   Every Mass induces a unique interaction between the Second Person and the world, especially at the consecration and at the reception of Communion.  Jesus makes repeated reference in the gospels to his relationship with the Father, claiming, for example, that the Father and He are one, and that the Father had sent Him.  In Chap. 1 of the Acts of the Apostles Jesus mentions that he will send the Holy Spirit, and Chap. 2 describes the arrival of the Holy Spirit at Pentecost.  The Holy Spirit inspired the apostles to proclaim the gospel message. 

 

          A number of theologians have commented on the inhabitation of God in the souls of the just. Augustine considered this indwelling as trinitarian, but with the Holy Spirit playing a special introductory role.  Thomas Aquinas asserted that both the Son and the Holy Spirit dwell in the soul by grace, and both of them are invisibly sent.  He considers the Father as also dwelling in us by grace, but not as having been sent from another. The rationale why a divine person is in a rational human nature in a novel manner involves sanctifying grace.  Th. De Régnon believes that each divine person sanctifies the just soul in his own unique manner, establishing a special relation with the soul, H. Nicolas asserts that God as Trinity is present in each soul by personal relations of knowledge and love.  Réginald Garrigou-Lagrange (1877-1964) explains the special presence of the Trinity in the just as involving sanctifying grace, infused virtues, and the seven gifts, which the soul can enjoy through a connatural intimacy with the inner life of God. 

 

          There are three ways to view the indwelling presence of God in a human soul:  1) God is the principle of our supernatural life, the cause of sanctifying grace,  2) God is the term of our supernatural life, with knowledge and love the reason for the indwelling, and  3) God is both the principle and the term,  He is both the cause of supernatural life, and the object of special filial knowledge and love. 

 

Go to Top

8.  STRONG AND WEAK INTERACTIONS

 

          In physics the interaction between two entities is called strong if the two entities are appreciably influenced by the interaction, or if the interaction has a major influence on other acts or operations. In the language of scholastic philosophy, we say that such beings are substantially or essentially affected by the interaction.  The interaction between beings is called weak if it has only a negligible or minimal influence on other interactions of the interacting beings.  In particular such a weak interaction will not appreciably influence the internal (ad intra) interactions of the two entities.  In the nomenclature of scholastic philosophy we say that such beings are affected in a nonessential manner, or per accidens.  Relative to the internal dynamical life of the Trinity all operations ad extra are weak interactions, although in relation to particular beings in the world they can be strong.  When Jesus healed a leper God was not changed, but the leper was very much changed.  The extent to which one of the Divine Persons interacts with the world has no effect on his mutual internal life of circumincession, on his divinity, or his omnipotence. 

 

9.  MISSION AND APPROPRIATION OPERATIONS

  

          We may distinguish two types of ad extra operations.  In the first type called a mission operation one particular divine person plays a dominant role, as in Confirmation, and the other two persons play more secondary roles;  in the second type called an appropriation operation all three divine persons play comparable roles.  The Incarnation, Redemption and Resurrection were mission operations involving the Son, and the coming of the Holy Spirit at Pentecost was a mission operation of the Holy Spirit.  According to a viewpoint common to many of the Greek Fathers of the Church the Father is referred to as the Creator, the Son as the Savior, and the Holy Spirit as the Sanctifier. Scholastics, on the other hand, emphasize that in divine operations ad extra such as creation and sanctification the three persons act jointly, the Father through the Son in the Holy Spirit (Pater per Filium in Spiritu Sancto omnia operat), so these are appropriation operations. The Catechism of the Catholic Church (#689) refers to the joint mission of the Son and the Holy Spirit sent by the Father to the world. 

 

          In the sixth century Fulgentius of Ruspe mentioned two missions of the Holy Spirit sent by the Father and the Son:  when He came on the apostles as fire, and when He came over Christ in the form of a dove.  M. Scheeben suggests that the divine missions are temporal prolongations of eternal processions.  B. Lonergan observes that the Son is sent to restore and reconcile all so God may be all things to all, and the Holy Spirit is sent to preside over the whole Christian life of each of us in sanctifying grace.  He further asserts that the object of a mission involves the cooperation of others, establishing personal relations like friendship. 

 

class=Section2>

 

Go to Top

10.  DYNAMISM OF THE TRINITY

 

          The air in a calm room is in reality composed of nitrogen, oxygen, and other molecules darting about at high speed in all directions.  The occupants of the room are not aware of this rapid motion which is random in magnitude and direction.  Only coordinated motion of air such as wind is detectable without the use of sophisticated instruments.  From a more general viewpoint we say that the material world has a microscopic or small scale dynamism which often produces a static behaviour on the macroscopic or large scale level of observation.  In theological terminology we say that the material world has an internal or ad intra dynamism which produces an observable external or ad extra appearance.  By analogy with this reasoning we can say that ad intra God as a Trinity of three persons is ever interacting, while ad extra God seems to us as ever the same, with the world ever changing.  The dynamism of the world does not react back on or have any appreciable influence on the ad intra life of the Trinity. 

 

11. TRADITIONAL EXPLANATIONS OF THE TRINITY

 

          Down through the centuries various theologians have thought about and written about the Trinity, and their understanding of it.  This was especially the case during the fourth and fifth centuries when the first four Ecumenical Councils Nicaea 325, 1 Constantinople 381, Ephesus 431, and Chalcedon 451 were convening to resolve the issues of Jesus Christ being true God and true man, and of God having one nature and three persons.  After the latter issue was decided there was still a great deal of interest in trying to comprehend the meaning of the trinitarian doctrine.  The main controversial issue was the filioque (and from the Son) question, whether or not the Holy Spirit was descended from the Father and the Son.  This issue was finally decided in the year 1215 when the 12th Ecumenical Council (Lateran IV) decreed in conformity with the Athanasian Creed that the Holy Spirit proceeds from the Father and the Son.

 

          The Eastern Church led by the Cappadocians Gregory of Nyssa, Gregory of Nazianzus, and Basil  tended to stress the plurality of God, and the Western Church with Athanasius as their spokesman put more emphasis on the unity of God.  The final definitive understanding that was arrived at was in part a result of the tension between these two opposing, but still orthodox, viewpoints.  The Church Fathers argued about a single letter, a Greek iota, in deciding that the Father and the Son are homoousios, that is they have the same (homo) rather than similar (homoi) natures (ousioi).  Victorius suggested as an analogy of the Trinity the fact that the soul of man exists, lives and understands (esse, vivere, intelligere);  Augustine suggested several analogies, such as:  a) lover, beloved, their love;  b) being, knowing, willing;  c) memory, understanding, will;  and d) mind remembering God, mind understanding God, mind loving God.  Augustine proposed a so-called  psychological theory of the processions in the Trinity that Thomas Aquinas perfected  by affirming that the Son is born of the Father as the word of the divine intellect, and the Holy Spirit proceeds from the Father and the Son as a procession of love. 

 

          In the twelfth century Joachim de  Fiore (c.1132-1202) divided the history of the world into three epochs: the time under the Old Testament law is ascribed to the Father, the subsequent time under the gospel is ascribed to the Son, and future time under spiritual intelligence is ascribed to the Holy Spirit.  Later that century Albertus Magnus (c.1200-1280) talked about a divine communicability acting ad intra that is involved in the generation of the Son and the spiration of the Holy Spirit.  Joachim de Fiore discussed the Trinity as a quaternity of three persons with their common essence as a fourth.  Thomas Aquinas mentioned four real relations identified with the divine essence: divinity, paternity, filiation or spiration, and procession; three of them paternity, filiation and procession are distinct by mutual opposition and hence constitute the three persons.  Duns Scotus (1265-1308) maintained that there are seven real relations in God, namely: paternity, filiation, active and passive spiration, identity, equality and likeness.  Alexander of Hales (c.1185-1245), teacher of Bonaventure (1221-1274),  discussed a twofold diffusion of divine goodness, namely a personal type whereby one person diffuses in the procession of another, and an external type in the communication of divine persons to creatures. 

 

Go to Top

12.  RECENT SPECULATIONS ON THE TRINITY   

           There are a number of newer, more speculative viewpoints on the Trinity that call attention to the diversity of ad extra operations attributed to individual divine persons.  For example, J. Macquarrie suggests that 1) the Father is the Primordial Being communicating Himself with the world, 2) the Son is Being which has been communicated and expresses itself through creatures, and 3) the Holy Spirit reconciles and unites all beings with Being.  For R. C. Neville:  1) the Father is identified with the creator, 2) the Son is “the determinate product of the creative act in its character as the normative expression of the creator”, and 3) “the Holy Spirit is the creative act itself mediating normatively between the creator and the product.” J. N. D. Kelly conjectures that 1) the Father refers “to man’s absolute future”, 2) the Son “calls all men to accept God as their absolute future”, 3) and the Holy Spirit is “God’s love communicated to man to enable him to accept God as his future.”  These three speculative theories all express God’s interactions with the world in terms of three inter-related and well coordinated mission operations: 1) a Father-world mission operation, 2) a Son-world mission operation, and 3)  a Holy Spirit-world mission operation.  However the inter-relatedness of some of the operations in these theories suggests that they do not all correspond to a person acting in isolation, that is they are not all pure mission in nature, but have some admixture of an appropriation character. 

 

          Pierre Teilhard de Chardin (1881-1955) viewed creation as a reflection or image of the Trinity. Karl Rahner (1904-1984) claims that the two divine processions have something to do with the two basic acts which belong to the spirit, namely knowledge and love.  Bernard Lonergan (1904-1984) asserts that the three divine persons are not only referred to each other by interpersonal relations, but in addition they are constituted as persons by these relations.   M. Schmaus maintains that the tri-personality of God is a sign of life at its fullness, with a continual exchange of life between the three divine persons, each finding his existence and joy in the personalities of the other two.  B. Cooke stresses the community of persons, with the divine being God continuously constituted by the dynamic personal communion between the Father, Son and Holy Spirit.  Matthias Scheeben (1835-1888) suggests that each of the divine persons is in His own manner both a center and a focus to which the other two are related,  and in which they are united to each other.  For example, the Holy Spirit unites the Father and the Son in and with himself as the product of their mutual love.  G. Salet stresses that each divine person possesses an infinite richness which he communicates to the others in an unselfish manner, loving the others in a total giving of self since it is in the other two that he finds himself. 

 

Go to Top

13. CHRISTIAN PRAYER

 

          Devotion to the Trinity has always been an important emphasis in the Church’s devotional life.  We start our prayers by blessing ourselves “In the name of the Father, and of the Son, and of the Holy Spirit.”  Traditional prayers like the Te Deum, and traditional hymns like the Pange Lingua, refer to the Trinity.  Many of the hymns in the Liturgy of the Hours or Divine Office end with verses that sing praise to the Trinity, such as:. 

 

                                                Sit, Christe, rex piissime

                                                tibi Patrique gloria

                                                cum Spiritu Paraclito

                                                in sempiterna saecula.  Amen.

 

The Mass has many references to the divine persons.  Thus devotion to the Trinity has always been central in our lives of prayer and worship, and the more acquainted we are with the nature of the Trinity the more devoutly we can pray and worship. 

 

Go to Top

14.  IRREDUCIBLE TENSOR MODEL

 

          There is a mathematical formalism involving irreducible tensors and group theory which has been used to explain many aspects of physics during the past century.  This formalism is a mathematical method for treating a set of entities which exhibits both a fundamental unity and a well characterized diversity.  The set has a unifying principle, and the individuals that comprise the set have a differentiating principle or property.  There is an operator called a raising (or lowering) operator which can derive the individual entities from each other.  For example, the nucleus of an atom is composed of several or many nucleons, and the nucleons come in two types, a positively charged proton and a neutral (i. e. uncharged) neutron, each of which has a particular mass. These two nucleons are related to, and can be generated from, each other by raising and lowering operations.   This mathematical formalism is briefly described in the Appendix, and then applied as a model to explain the manner in which God can be simultaneously one in nature and threefold in persons.  The rationale that motivates proposing this model is what motivated St. Anselm (1033-1109) in the 11th century, namely:  fides quaerens intellectum, the name of this website.  Many of the principal features of our understanding of the Trinity fit well into this mathematical formalism, and the results complement traditional theological explanations of the Trinity.  Since these results are couched in mathematical expressions, it would break up the continuity of this presentation to elaborate on them here, so the appendix should be consulted for details.    

 

15.  DISCUSSION

 

          We have maintained that there is a valid distinction that can be made between the immanent Trinity which refers to God as He is in Himself, triune in mutually interacting persons without reference to the world, and the economic Trinity which refers to God as manifested to or interacting with the world.  It is not clear that theology will ever be able to elucidate operations whereby individual persons of the trinity interact with the world, although theologians have distinguished between individualized mission operations of particular persons, and collective appropriation interactions of all three persons acting in unison.  Our emphasis on dynamic ad intra interactions is a shift from the traditional Thomistic view of the Trinity to one  more in the spirit of Bonaventure and Scotus. The present stress on mission and appropriation operations is more in accord with the spirit of Rahner than it is with traditional Thomists.  Our highlighting of the economic Trinity is in contrast to a traditional emphasis on the immanent Trinity and the procession operations. 

 

          It is hoped that the exposition in this chapter will assist believing Christians in their lives of prayer and worship, and that it will provide some insight to Nonchristians concerning the place of the Trinity in our lives.  Perhaps the exposition on these pages will help to clarify why a Christian scientific mentality can be attracted to probing into the mysteries surrounding the triune nature of God.   It is fitting to end with a quotation from the Sulpician priest Adolf Alfred Tanquery (1894-1932) whose theological writings educated most of our seminarians for several decades during the 20th century:  “Pater per Filium in Spiritu Sancto omnia operat.”

 

Go to Top

APPENDIX

 

IRREDUCIBLE TENSOR MODEL OF THE TRINITY

 

          The irreducible tensor formalism is a mathematical method used in quantum mechanics for treating a group of entities which exhibits a basic unity as well as a characteristic diversity. We use the notion of what we call a wave function to designate all the information that we can know about the entity.  The wave function has the symbol R, the Greek letter lower case psi.  A superscript g is used to designate the wave function Rg of the group, and a subscript i is added to denote the individual member of the group, corresponding to the notation Rgi.   In our case the group is the Trinity RT, and the individuals RTP are the Father, the Son, and the Holy Spirit whom we can designate by the wave functions   RTF    = RT+1 ,    RTS   =   RT0 , and   RTHS   =  RT-1 .  In writing these expressions we follow standard quantum mechanical nomenclature by designating the first individual or person F of the group by the number P = +1, the second individual S by P = 0, and the third HS by P = -1.  Thus we have

 

                                      P = +1              Father               RTF    =  RT+1

 

                                      P  =  0               Son                 RTS    =  RT0

 

                                      P =  -1         Holy Spirit           RTHS    =  RT-1        

 

The letter P might be called the person quantum number which can take on three possible values, namely +1, 0 and -1.       

 

          In quantum mechanics the wave functions in a group can be converted into one another by what are called raising and lowering operators, denoted by R and L respectively.   For a wave function RM with the subscript M which is either an integer or a half integer, these operations produce the following results

 

                                                          R RM   =  RM+1

 

                                                          L RM   =  RM-1      

         

In the case of the Trinity we have

 

                                                          L RT+1   =  RT0

 

which corresponds to

 

                                                          L RTF   =  RTS

 

The quantity L might be called the begetting operator since by this equation the Father generates or begets the Son.  More technically we say that the begetting operator operates on the wave function of the Father and produces the wave function of the Son.  In less technical language the Son is begotten by the Father. 

 

          The spiration operator can be designated by (L)2, and it operates on the Father and the Son as to produce the Holy Spirit as follows:

 

                                      (L)2 [RT+1   +  RT0 ]   =   L [ L ( RT+1   +  RT0 ) ]

 

                                                                       =   L  [ RT0   +  RT-1 ]

 

                                                                       =    RT-1   +   0  

 

                                                                       =    RT-1   

 

Symbolically this can be shortened to the expression

 

                                                (L)2 [RTF   +  RTS ]   =    RTHS  

 

meaning that the Holy Spirit proceeds from the Father and the Son.  The Orthodox Churches prefer the expression

 

                                                         (L)2 RTF    =    RTHS  

 

whereby the Holy Spirit proceeds from the Father alone.  In this case there is still the intermediate step in the mathematical development of the equation

 

                                                (L)2 RTF    =    L  RTS   =   RTHS  

 

which involves the Son and points to the filioque. 

 

          This irreducible tensor approach does not really prove anything, but it does show that there exists a mathematical formalism capable of describing the basic defining ad intra operations of the Trinity. 

 

 

Go to Top