Wednesday, December 15, 2021

Christian Ontology: Understanding the Mathematical Formula by Which One May Teach Trinitarian Theology





Christian Ontology  

Understanding the Mathematical Formula by Which One May Teach Trinitarian Theology




I. Introduction

II. Philosophical Foundations: Language and Ontology

III. Trinitarian Theology

IV. Exploring the Mathematical Formula by Which One May Teach Trinitarian Theology

V. Christian Ontology: Immanence and Transcendence, Christology, and Ecclesiology

VI. Conclusion



Introduction


Islam is the other major western monotheistic religion with a proselytizing mission.  Muslim missionaries have a much easier job selling monotheism to possible converts, because they are no nonsense monotheists.  The Christian belief concerning the Trinity is easy sport for a muslim missionary, because on it’s face it doesn't seem to be monotheistic at all.  To assert that three persons abide as one God seems like the ultimate attempt to “have your cake and eat it too” by sheer will of faith.  It also seems to smack of theological laziness.  The narrative of unbelievers implies that Christians wanted to say a lot of thing, “God is one”, “Jesus is God”,  “Jesus Prays to God”, “Jesus is Human”, “Wait . . . Maybe the Holy Spirit is God too . . .”.  The implications is, at some point, Christianity said you need to believe all these things at the same time, and the dogmatic philosophical cop out/catch all is the adamant belief, against all data, experience, or reason, is the dogma of the Trinity.  


The purpose of this treatise is to explore trinitarian theology by means of ontology as opposed to mathematics.  With this methodology the hope is that the deep mysteries and paradoxes of The Church will be more comfortable for the believer.      

We will begin with a philosophical foundation.  In the first section we will explore how language is inadequate when trying to describe the nature of God.  From there we will explore the nature of Christian ontology, an ontology which bridges atomism and monism.  We shall explore the nature of objects and relationships and assert that Christianity’s fundamental ontological position is that objects and relationships are equally real. 

Following that we will apply Christian ontology to trinitarian theology and come to a basic comfort level with the dogma of the Trinity. This section will end with a cognitive meditation that allows the reader to experience Christian ontology phenomenologically and thereby come to an experience of the trinitarian image and likeness of God within themselves.   

After this we will apply our ontological exploration to mathematics and explore the mathematical formula by which one can teach trinitarian theology. We will learn that our problem has never been math, but ontology. God is fundamental to reality and reality is fundamental to math.  Knowing this eases our discomforts with the dogma of the Trinity which spring from our assumption that math is fundamental to reality and reality is fundamental to God.

  The final section will be a survey of how Christian ontology, which is properly developed from the dogma of the Trinity, expresses itself in other deep mysteries of Christianity.  In this section we will make a cursory study of God as immanent and transcendent to creation, Christology, and ecclesiology.  


With this treatise the hope is that the dogma of the Trinity will cease to be a peripheral teaching that inspires fear in the Christian who seeks to appear intelligent.  Instead, with the ontological as opposed to mathematical lens, the dogma can takes its place as a central and all encompassing belief of the practicing Christian.           



Philosophical Foundations: Language and Ontology



Idolatry of Image and Idolatry of Word


How we approach God is a delicate art.  Revelation assures us that God is accessible, yet at the same time God is transcendent and ultimately mysterious.  The charge of the iconoclast is that any image of God that is made is not accurate, and therefore an idol, a false god.  In a sense the iconoclast is technically correct.  If one worships an image as God, or presumes that an image is truthfully accurate, it is what God actually looks like in his entirety and in his essence, they are in error.  But humans are in need of access to God and as was discussed in both Sacramental Cosmology and in Intuitive Ritual Investment and Conscious Ritual Investment God uses the world around us, including our art and action in order to afford us access to him in a way that our limited understanding can grasp.  

In this treatise the access we are seeking is knowledge, which is different than access to grace.  We are seeking to understand something about God, “how can we understand God as three persons and one God?”  Art is useful in this endeavor as well, yet in our post enlightenment rational culture, the privileged conveyance for “knowledge” is language.  Because of our bias toward the linguistic it is hard for us to come to terms with the fact that the limits of our grasp of God is not just relegated to physical images, but concepts and definitions as well.  If they aren’t really true of God, then they are false images.  If they are taken as completely accurate, or describing God completely, they are false gods. 

Just as we cannot make graven images of God that accurately reflect who God is so to with our language.  The first three commandments require the believer to take an apophatic stance.  The second commandment forbids total investment in physical representations of God.  The third commandment forbids total investment in any verbal representations of God.  Taking the name of the Lord in vain was an offence punishable by death according to levitical law, and the seriousness attached to it revolved around the question of use.  Are you going to presume to know the proper way to use God’s name?  To use God’s name assumes the speaker has some power over God, that the speaker understands God in such a way as to be able to speak for him.  To name something gives one power over it, the ability to shape the idea of what it is in other people's consciousness and the ability to call it or command it.  To see a prime biblical example of absolute verbal authority one need read no further than the first part of Genesis.  First God makes creation in Chapter 1 by means of his words, next in Chapter 2 the Lord names the human, Adam, then brings the animals to him to be named, giving him dominion over them.    

Our words are not like God’s true existence.  They are powerful, but not supremely so.  The author of Exodus make comic use of the inadequacy of human words in the beginning of the book of Exodus.  The pharaoh is gives decree after decree with absolutely ineffective words.  Even when his orders are followed, the result is not his desire.  This is obviously to be juxtaposed to the absolute potency of God’s Word, and Pharaoh’s arrogance as it plays through the story is a cautionary tale for all of us especially considering that in the course of the story God’s “Name” is revealed to Moses and the Israelites.  The name itself is extremely enigmatic and less of a name as it is a description of God’s ultimate nature which extends beyond our experience.  The Jewish people were so cautious with the use of this name the observance of the second commandment meant that except on rare occasion no one even mentioned the name.


This leads to the present time, where even a cursory look at politics, academia, advertising, the business world, almost any field will betray a host of “terms of art”, technical language, logisms and neologisms demonstrating the agreement we have with the power of words and language.  Amid all the languages that we have our most powerful and most perfect language is mathematics.  Our western culture is completely enamored with mathematics.  We see it as the language that is all that a language should be.  It is unambiguous.  It works every time with complete predictability.  There is no vagary in math.  The systems of formal and symbolic logic we have developed over the past century and a half are simply attempts to reduce all language to math. The upshot of this is, starting with Bertrand Russell's Principia Mathematica, the ability create computer languages and programs.  When it is all boiled down, the objective of the hard sciences is to translate reality into numbers and mathematical relationships.  This is most obvious in the foundational science of physics, but not much less obvious in chemistry and the genetics of biology.  Interpreting reality through math and seeing math as the foundation of reality itself  is not new, Pythagoras in the ancient world had the same idea, but what is new is the pervasiveness of the idea in our culture.  Because of our view, to say that math is a language is off-putting.     

The pervasiveness of math in our ontological view is what makes the doctrine of the Trinity so hard to allow in our minds.  The Catechism states that all words fall short of the glory of God, “God in his essence is beyond human description”, a very apophatic, via negativa kind of statement.  Most people would probably immediately agree, knowing that God is mysterious and powerful.  But once a person starts applying that assertion to the ways we gauge certainty or the way our language fundamentally works it gets really uncomfortable.  In this treatise we are going to start apply this assertion to mathematics and no one likes to do that.  Can you apply math accurately to God?  Is God bound by mathematical rules?  Can one really and accurately say “God is One”?  Christianity without doubt says “YES!” . . . and “kind of” . . . and “no” . . . and at this point everyone walks away.  Not just because of the indecisiveness, but because the way the conjunction “and” is used here.  God is one and three.  That doesn’t hold with how mathematics works and since math is the language we feel is the most fundamental and clear way to describe reality, we don’t like that it does not apply to God.  If it doesn’t apply, he must not be a reality, or at least not in the way that is contradictory to math.  But God is not clear, nor is he, in his essence, knowable simply by use of clever language.  I am not a mathematician, but I believe that math can be used to teach trinitarian theology.  The trick here is that Math is not fundamental to reality, reality is fundamental to math.  Therefore, the questions of trinitarian theology are not mathematical but ontological.   

This treatise is not about to describe the inner workings of God.  No one can.  We can’t make the reader understand the mathematical mystery of God.  What we can do is make one so uncomfortable with reality itself that the notion of the Trinity fits right in.  In order to do that we must grasp the thought of the western hemisphere and the eastern hemisphere, synthesis them, place them in ancient Greece and develop an ontological view of the world that is reflective of everyday experience and accessible, though mysterious.  After this we will explore the mathematical formula by which one may teach trinitarian theology.  If I showed the formula to you now, you would say, “I understand the math, but what does it have to do with the Trinity?”  If we are successful in our endeavor, by the end you will look at the formula and say,”I see how it relates to the Trinity, but now math doesn’t make sense.”  The discomfort will no longer be with God as one and three, but with math and how it relates to reality.  But that is a better position, because as a professing Christian God should be more fundamental to existence than math.  



Ontological Conflict


When one explores the nature of God, the only access one has to God, the artist, is creation, his art.  You can learn about an artist from their art.  Though you may not get everything, you will learn things that the artist sought to convey and those things are most likely important to the artist.   For our exploration of the dogma of the Trinity we are going to start with reality.  The concept of the Trinity seeks to convey something fundamental about the nature of God, thus we are going to look as best we can at the fundamental nature of reality, we are going to survey varying ontological philosophies.  Where does reality lie? What is not real or at least not considered when discussing reality?  The basic question to be answered is the question of ontology  “what is real and what is not?”  or maybe even “less real”.  What is the basic nature of reality itself?  An extremely brief sketch of how we in the west view the ultimate nature of reality in the modern world would be of service to us.  

What seems to have happened over the last four centuries is the rise of an atomistic world view.  In ancient Greece this view was first put forth by Luccipus and Democritus.  Atomism states that reality is ultimately made up of some sort of fundamental unit, an atom.  That unit is unsplittable and when atoms collect together, by their congregation, they form other objects which are more  and more complex the bigger they get.  

Objects are the key interpretive lens of reality for atomism, starting with the fundamental objects, the atoms themselves.  Relationships in this view are seen as illusory, simply the collection of objects.  Objects, on the other hand, are the “real” thing.  Epistemologically they are considered “real” because they can be quantified and measured.  The reader can already see how atomism fits quite well with an empirical, scientific, worldview.   There is a nice joining of the atomistic view with the neo-pythagorean view of reality being reducible to numbers. Objects can be quantified, 3 atoms, or three people or three countries or three gods.  

Relationships are harder to quantify, it doesn't linguistically sit well to say Bob has three loves, or there are three trusts in a situation.  It’s easier to understand Bob having three kinds or types of love or trust, but there really is only one love.  Which leads us to the view of reality more dominant in the East.  That view centers more on relationships to the point of all reality being one relationship.  We will call this view Monism and the end result is to view all reality as one object, there is no true distinction between you and your environment, individuated objects are illusory.   In Ancient Greece this view was put forth by Parmenides and is much less comfortable to the Western mind, and therefore probably to the reader.  The methodology of western scientific mind operates by making distinctions and classifications, not by destroying them.  The stereotypical Eastern mind is more mystically geared and seeks dissolution into the ultimate by loss of individuation. 

Very few people live their practical lives in the extreme of either of these philosophical views.  These distinctions are usually only trodded out in academic debate or discourse that is more sport than pedagogy.  But their assumptions do impact society.  When a cultural conflict on where reality lies arises, the inconsistencies are debated, though not usually at this fundamental of a level.  The debate itself is commonly known in philosophy as “the problem of the one and the many” and has a deep and many varied history.  It is one of those metaphysical questions that most western minds simply dismiss as useless, but  western minds only see it as useless because we have chosen our side and stick with it, so there’s no need to debate.  It becomes difficult when the issue crops up and we are forced to consider the question, we ignore the problem of the one and the many so much that we are not used to contemplating it, and therefore our attempts to live succinctly are novice and inconsistent.  

Here’s a classic run through of how the issue works.  I am standing in my classroom with students and I ask “What is this thing?” as I point to an empty desk and the answer comes back, “its a desk”.  No one would argue that, but if I wanted to play the sport of philosophy I could smugly reply, “Ah! You think that, but it’s really a collection of wood, metal, and a little plastic!”  There would be a collective moan, but probably no one would disagree.  What I did was break the desk down to it’s simpler elements, elements that are closer to the most basic element, which according to the atomistic view is where reality lies.  In fact if I kept going I could ultimately retort, “You say it’s a desk, but really it’s simply a collection of atoms”, or “subatomic particles” for that matter (a phrase that etymologically does not make sense).  Once again, the only real resistance you get to this sort of thing in the western mind is, what is the purpose of pointing that out?  Especially in America we are pragmatic with our philosophy and want an end use, so nanotechnologist, particle physicists and other such people may need to worry about that, but the rest of us can just agree that a desk is a desk and get on with our lives.  The point is we do agree.  Given how our thought has developed over the past few centuries, anyone who fundamentally disagreed would bear the burden of proof if they wanted to pursue the argument. 

      

Now let’s take the opposite tack.  “What is this thing?”  “It’s a desk!”  “Ah! You think it’s a desk, but it’s really only part of the classroom!”  This time the monist position is followed in the opposite cosmological direction; part of the room, part of the building, part of the city, part of the country, part of the world, solar system, galaxy, universe etc.  Also this time it is much less likely that there would be quick but dismissive acceptance.  Instead of going down to atoms this line of reasoning takes one all the way up to the ultimate expanse of reality.  “You think it’s a desk, but it’s really only part of the oneness of reality.”  In the first instance the western mind generally sees the arguments as nit picky but correct.  In this case, the western mind generally sees the argument as at best metaphysical, and therefore suspicious.  But more probably such a line of reasoning would be met with absolute scandal and rejection.  Not on logical grounds, or on grounds of evidence, but simply because we just don’t think about reality that way.  The arguments for the ultimate nature of reality are equally mysterious going up the chain of existence or down when taken to their conclusion. Ontological inquiry is equally metaphysical when reaching for the atom or the cosmic.   It’s just that the atom as the definer of what is “real” is more comfortable to the western mind  than the cosmos.  

The truth is that both of them break down at the extreme.  If you adopt the atomistic view and begin the division process, you will quickly find that you can always divide further.  Hence after atoms (the unsplittable) we have subatomic particles, you can always categorize and split further and further.  If one adopts the monistic view the very experience of perception keeps us at a distance from at least everything we perceive as apart from us.  The way the human mind works seems to presume distinction.  Hence in the East you encounter a host of religions that seek to quiet or calm the mind to the point of perceptive annihilation.  Neither seems right in the extreme and neither addresses our everyday experience given that the end point of their speculation is either too far “down” or too far “up”.


In our culture wars you can see the problems that this mystery of reality can cause.  One prime example is the abortion debate.  When this topic comes up I always point out the principal question to be answered is, “What is a human?”  Figures and statistics are useless when measured up against this issue.  All the effective debate revolves around this question and once one defines this, one has the answer.  No one wants to destroy innocent human life, so the only way one can justify abortion is to define the object not as a baby (human) but as a fetus (biological object / tumor).  That object is simply part of a greater system, the female body, not a real entity in and of itself.  The object is illusory and the relationship that binds that object to the primary system, the object defined as a female human body, is real.  

One problem in popular discourse on the issue is that people don’t delve as deep as the human question.  Most of the debate revolves around health statistics or pictures of the fetus coupled with emotive appeals.  These things dance around the issue but do not confront the fundamental question.  In fact if one takes atomism or monism to the extreme a “human” isn’t real under either position.  A human is either “just a collection of atoms”  or “just part of the universe”.  One way one can look at much of the most metaphysical philosophical speculation over the last two and a half millennia is how great thinkers have been trying to reconcile these two fundamental views of reality, often simply in order to define what a thing is, like for example, a human.  There seem to be real objects and there seem to be “objects” manufactured by means of mental construct.  How do you tell the difference? Is a human real or just a system of organs, or just a collections of cells or just a collection of atoms?  OR just part of a family, part of a city, state, nation, culture species, an example of a mammal, part of biomass in toto, part of the cosmos?  So as we look at the pregnant woman there is the fundamental ontological question, is she one person or two?  Pro-life says two, pro-choice says one.  Though extremely abstract, it turns out to be a question of great importance, because lives are, or may be, in the balance and how you answer matters. So where does reality lay? how do you know an object is real in and of itself, or simply part of another more primary or “real” object?  We cannot think about this all the time, so we go with our assumptions until they are challenged, and even then we don’t like to get fundamental with our probing of reality.


Christian Ontology


As abstract as the fundamental probing of reality may seem, this is the exact type of question brought to bear as Christians came to unpack the experience of Christ in a monotheistic religion.  Quickly he was revered as God, but God is one.  Also Jesus is human, but God is not human and humans are not God.  This is obviously a tangled problem.  If you make a peripheral study of the issue, what it looks like is a set of dogmas to be blindly believed, defined so that we can say all these inconsistent things at the same time without reference to anyone’s everyday experience.  The early defined dogmas concerning the nature of God and Christ come of as a bunch of labyrinthian assertions that, when questioned, always ends with, “because we said so.”  or “that’s just how it is.”  However with a slight ontological shift, all the great mysteries of Christianity can be absolutely relatable to how we experience our daily lives.  The problem is that we tend to ignore vast realms of how we experience our lives to the point of denying them.  It’s not that you can explain the mysteries, it’s just that day to day reality is far more mysterious than we like to admit, the Christian mysteries aren't unique examples of absolute mystery, they are simply indicative of how mysterious our day to day experience is.  Our problem is we tend to ignore mystery when we are uncomfortable with it.


How Christian ontology works, or at least how it’s supposed to work, is clearly laid out in the New Testament in many ways, but most easily by a series of analogies. I’ll use the most popular two in order to get the example across.  First,  John 15:5a “I am the vine, you are the branches.”  In this passage Jesus is talking about how a disciple bears fruit and in doing so he reminds the listener that he and the listener are bound like a vine and a branch. In a move that St. Patrick is said to have taken in teaching Christian ontology 300 years later, Jesus employs a plant analogy.  Look there’s a vine (object) and there’s branches (objects) but they are in relationship in such a way that the branches need the vine to live.  For our purposes, however, it is all one plant.  Here you have the crux of Christian ontology, reality is simultaneously simple and manifold.   The question is where does reality lay?  The answer is “everywhere.”  An answer that seems completely obvious, obvious that is until philosophy is brought to bear.  Reality lies both in the parts and the whole.  For this to make sense to a Westerner he has to invest in the idea that relationships are as real as objects.  This is harder and harder in a world where empirical measurement is a major criteria for substantiation because you can’t empirically measure a relationship.  Thus due to the nature of our discourse relationships are often assumed to be less real than objects.  Once again, not consciously by most people, it’s just the operative idea in our thinking and way of regarding life.  This is why the reaction to the stance, “the desk is simply part of the classroom” is so vehement. 

Paul’s analogy is even better known and more accessible, “As a body is one though it has many parts, and all the parts of the body, though many, are one body, so also Christ.” 1Cor 12:12.  Here Paul in the simplest terms demonstrates Christian ontology.  No one doubts that you have one body, and that there are many parts to that body (simple and manifold).  It’s the same for the Christian community which is really one thing, bound inextricably by a true relationship into oneness, but still has distinct parts, it’s member Christians.  This happens by means of the truest binding relationship for human beings, love, the relationship that can make a multitude of people one reality.  As Pierre Teilhard de Chardin says, “Love is the affinity which links and draws together the elements of the world.  Love, in fact, is the agent of universal synthesis.”  Sin is the absence of goodness and proper relationship.  Christ came to heal that and Paul’s point is to exemplify the true oneness that comes from experiencing Christ’s redemptive love.

This is not just applicable to the Christian community.  The analogies are taken from nature itself in a very philosophically rudimentary way to teach a simple point about reality.  Once you accept that all reality is one and at the same time infinitely divisible and this can be experienced in any given object at any time all the mysteries of Christianity seem less foreign, random or forced.  


God is Primary and Fundamental, so the dogma of the Trinity is the primary and fundamental comment on how reality itself works.  The dogma of the Trinity asserts that God is simple and manifold at the same time.  The dogma itself is not complicated, God is one God in three distinct persons.  This is the case from all eternity.  The first question any semi-intelligent person might ask is “How”?  and always the Christian must retreat into faith and say, “He just is.”  But if this leaves an unsatisfactory taste in your mouth then you may want to point out that it’s not all strange.  Remember?  “It’s a desk!”  “Ah, but is it? or is it a collection of parts . . . Part of the room” etc.  Play the game, it’s not just academic, it’s a fundamental aporia.  If your conversation is amiable and honest, you have to come to the conclusion that everything we experience is simple and manifold.  It doesn’t help in explaining how, but it does make the belief much more palatable, because everything else you experience conforms to the same principle.  Even if your conversational partner wants to go to an atomistic or monistic extreme, they still can only validate that by saying, “that’s just how it is.”  There’s no way to prove such beliefs, there’s not even criteria to prove it.  

Augustine himself struggled with this very problem in De Trinitate Book 6. He falls on the atomistic side of the philosophical spectrum with regards to creation, and he struggles with how creation reflects the divine nature of unity and division.


all that is body is composed certainly of parts; so that therein one part is greater, another less, and the whole is greater than any part whatever or how great soever. For the heaven and the earth are parts of the whole bulk of the world; and the earth alone, and the heaven alone, is composed of innumerable parts; and its third part is less than the remainder, and the half of it is less than the whole; and the whole body of the world, which is usually called by its two parts, viz. the heaven and the earth, is certainly greater than the heaven alone or the earth alone. And in each several body, size is one thing, color another, shape another; for the same color and the same shape may remain with diminished size; and the same shape and the same size may remain with the color changed; and the same shape not remaining, yet the thing may be just as great, and of the same color. And whatever other things are predicated together of body can be changed either all together, or the larger part of them without the rest. 


Later in the same book he states,


all these things which are made by divine skill, show in themselves a certain unity, and form, and order; for each of them is both some one thing, as are the several natures of bodies and dispositions of souls; and is fashioned in some form, as are the figures or qualities of bodies, and the various learning or skill of souls; and seeks or preserves a certain order, as are the several weights or combinations of bodies and the loves or delights of souls.


St. Augustine was enamored with math, and took a pythagorean / atomistic view of reality.  But at the end of the book you can see that he seems to recognize some reflection of God in the ontological makeup of creation.    

With a tangible experience of reality as simple and manifold, we can now fill out our ideas on “how” God in God’s self is simple and manifold at the same time.   As we do it is important to remember that all of this is analogous language.  As stated earlier, no one can know the essence of God.


Thus far in the treatise we have discussed the inadequacy of language as an absolute for understanding God.   We hinted at the role our perceived “perfect language”, mathematics, in society  before we shifted our study to Ontology.  We began with the general question of the “one and the many” that causes the conflict in ontological study. We then asserted the Christian view of ontology, that reality is simple and manifold at the same time, that both objects and relationships are equally real.  We were careful to note that as is the case with any ontological view, it is impossible to “prove”.   

In the next section we will apply all of this background information to trinitarian theology and explore how the standard language used to discuss God as Trinity is ontological not mathematical, and is discussing reality, not formulas.

Once the fundamentals are established, the next section will visit matters of lesser concern.  We will explore a mathematical formula that can be used to teach trinitarian theology. It takes a recalibration to see God as fundamental to reality and reality as fundamental to math and not the reverse to make use of the formula but, as will be explained, with the proper understanding our problem is not with math, but bad ontology.

The last section will then apply Christian ontology in order to make the reader more comfortable with other deep mysteries of Christianity. In this section we will touch on God’s immanence and transcendence, christology, and ecclesiology.   

 


Trinitarian Theology



In the last section we attempted to develop the necessary philosophical foundation for finding comfort with trinitarian theology.  We explored how language is inadequate when trying to describe the nature of God.  From there we discussed the nature of Christian ontology, an ontology which bridges atomism and monism.  We also dwelt on the nature of objects and relationships and asserted that Christianity’s fundamental ontological position is that objects and relationships are equally real. 

Now we will seek to apply Christian ontology to trinitarian theology and come to a basic comfort level with the dogma of the Trinity. This section will end with a cognitive meditation that allows the reader to experience Christian ontology phenomenologically and thereby come to an experience of the trinitarian image and likeness of God within themselves.   

After this we will apply our ontological exploration to mathematics and explore the mathematical formula by which one can teach trinitarian theology. We will learn that our problem has never been math, but ontology, God is fundamental to reality and reality is fundamental to math.  Knowing this eases our discomfort with the dogma of the Trinity which spring from our assumption that math is fundamental to reality and reality is fundamental to God.

  The final section will be a survey of how Christian ontology, which is properly developed from the dogma of the Trinity, expresses itself in other deep mysteries of Christianity.  In this section we will make a cursory study of God as immanent and transcended to creation, Christology, and ecclesiology.  


The Father the Son and the Spirit


The difference between the Father, the Son and the Spirit are a difference of relationship.  There are two relationships that fold into one primary relationship that fold into the oneness of God.  These two are the relationship of begetting and the relationship of proceeding.  What’s the difference between the Father and the Son?  Going with the Creed , the Father begets the Son and the Son is Begotten by the Father.  What’s the difference between these and the Spirit?  The Spirit proceeds from the Father and the Son.  So how does one conceptualize that in a way that makes sense?  One of the  most useful pieces of information on that front is the traditional definition of the Spirit as the Love between the Father and the Son.  Begetting is what an object does to get another object.  Proceeding is what a relationship does between objects.  Thomas Aquinas makes use of a psychological model for describing the same assessment in the Summa P1 Q37 A1 the question is, “whether ‘Love’ is the proper name of the Holy Ghost?”


The name Love in God can be taken essentially and personally. If taken personally it is the proper name of the Holy Ghost; as Word is the proper name of the Son.

To see this we must know that since as shown above (I:27:2-5), there are two processions in God, one by way of the intellect, which is the procession of the Word, and another by way of the will, which is the procession of Love; forasmuch as the former is the more known to us, we have been able to apply more suitable names to express our various considerations as regards that procession, but not as regards the procession of the will. Hence, we are obliged to employ circumlocution as regards the person Who proceeds, and the relations following from this procession which are called "procession" and "spiration," as stated above (I:27:4 ad 3), and yet express the origin rather than the relation in the strict sense of the term. Nevertheless we must consider them in respect of each procession simply. For as when a thing is understood by anyone, there results in the one who understands a conception of the object understood, which conception we call word; so when anyone loves an object, a certain impression results, so to speak, of the thing loved in the affection of the lover; by reason of which the object loved is said to be in the lover; as also the thing understood is in the one who understands; so that when anyone understands and loves himself he is in himself, not only by real identity, but also as the object understood is in the one who understands, and the thing loved is in the lover. As regards the intellect, however, words have been found to describe the mutual relation of the one who understands the object understood, as appears in the word "to understand"; and other words are used to express the procession of the intellectual conception--namely, "to speak," and "word." Hence in God, "to understand" is applied only to the essence; because it does not import relation to the Word that proceeds; whereas "Word" is said personally, because it signifies what proceeds; and the term "to speak" is a notional term as importing the relation of the principle of the Word to the Word Himself. On the other hand, on the part of the will, with the exception of the words "dilection" and "love," which express the relation of the lover to the object loved, there are no other terms in use, which express the relation of the impression or affection of the object loved, produced in the lover by fact that he loves--to the principle of that impression, or "vice versa." And therefore, on account of the poverty of our vocabulary, we express these relations by the words "love" and "dilection": just as if we were to call the Word "intelligence conceived," or "wisdom begotten."

It follows that so far as love means only the relation of the lover to the object loved, "love" and "to love" are said of the essence, as "understanding" and "to understand"; but, on the other hand, so far as these words are used to express the relation to its principle, of what proceeds by way of love, and "vice versa," so that by "love" is understood the "love proceeding," and by "to love" is understood "the spiration of the love proceeding," in that sense "love" is the name of the person and "to love" is a notional term, as "to speak" and "to beget."



The Trinity is the self love of God, because a loving relationship needs a Lover and an Object of Love to exist.  Without at least two in a relationship the relationship cannot exist.  Each person of the Trinity is necessary if you want to use John’s definition of God, “God is Love.”  If the Spirit is not there they are not one and there is no love.  If either the Father or the Son are not there the Spirit could not spirate, to use Thomas Aquinas’ term.  The dogma of the Trinity states that God self loves from all eternity; in that God begets himself and loves himself.  Those are not illusory distinctions, or the Love itself would be an illusion, they are real distinctions.  The Father and the Son are truly distinct.  They are just bound into one by the relationship of Love that is the Spirit, making God one.   Remember of course that objects and relationships are equally real, thus the Spirit is also truly distinct and truly real. But all are one God.

 


 

It is easy, as a Western minded atomist, to say, “so the spirit is ‘just’ love”? as if love were somehow lesser or not a person.  Love is, as a relationship, as real as Father or Son.  And according to Christianity, if a person was what a person should be they ARE love, just as God is love.  In the west a person is more easily seen as a bio-unit, because we value objects as real and assume that relationships are fabricated concepts.  It is easy to take our analogical language of the Father and Son being “objects” and extend personhood to them, but hold that if the Spirit is “only a relationship” then that doesn't seem to be a true person.  Firstly, this takes the analogy too literally, secondly it does not respect what the Trinity teaches us about ontology.  To garner the lesson it may help to recognise where the opposite mistake is made. In Buddhism, the fundamental concept of Anatman, no self, goes to the opposite extreme.  The “self” is a series of impermanent relationships.  There is no object to call the self.  For a Christian invested with an ontology informed by trinitarian theology, both views are correct in a way, yet ultimately flawed.  

It may be helpful to put off contemplation of these mysteries and seek direct experience in order to garner a more fundamental type of knowledge.  To end this section we shall perform a cognitive meditation to garner an analogous experience of trinitarian existence.  We will use the psychological model of the Trinity to achieve this.

             

The Psychological Model for the Trinity

    

The psychological model for teaching the Trinity which would probably help us be more comfortable with God as self relational love because we can experience the mystery within ourselves.    This model uses the human inner experience as opposed to trying to figure out what’s going on in eternity with regards to begetting and proceeding or “proceeding” and “Spirating” as Thomas Aquinas phrases it.  Exploring this will make the trinitarian understanding of God much more relatable for the reader.  

To get started I must explain a little about the inner working of my head.  I am an auditory thinker.  I talk to myself in my head.  I assume most people think this way, but I am well aware that not everyone does.  However you may think primarily, by talking to yourself, in pictures, reading your thoughts as words on a page, it all works, but to cut down on redundancy I’m going to stick with my own experience, it’s the one I know best.   

I talk to myself in my head.  If I need to go to the store I say in my head, “I need cheese, I have to go to the store.”  In order for all this to happen  I have to speak, and I have to listen.  Or to put it another way there has to be a speaker and a listener in my head.  Those are two realities in my head, but there’s also  the “I” that is binding them together.  The relationship of I, or self perception, is so tight that I cannot conceive of there being separate realities in my head, though the speaker and the listener are distinct “things”.   Psychologically I am a self-relational being.  If you think in pictures there has to be a picture and an observer, if you read your thoughts, there has to be a writer and a reader.  In all these cases the dyads must be bound in a conscious, self aware,  relationship.   If you want to be a bit more first person and closer to the trinitarian language you could say I beget my words and listen to them in love.  Here you have the trinitarian self-relationship.   But even though those three are really distinct (hearer / speaker / self-awareness - The Father/ Son / Spirit)  I would never conceive of myself as anything other than one consciousness.  


Figure 5- Psycological Model.jpg

This psychological model is much more accessible to the modern mind and shows us one of the ways we are in the image and likeness of God, in that we are self relational like the trinitarian God is.  It also demonstrates that the trinitarian model, and the ontology assumed by it,  is the only way you could have a self-aware and personal God.  The other abrahamic faiths that have what we might call a “strict” monotheism and a transcendent focus, and winds up with a theologically static ultimately transcendent God.   Whereas, the eastern traditions have an ultimately immanent view of ultimate reality that collapses into reality itself and becomes an impersonal substance and/or force that begets reality by means of overarching law and without recourse will or love.  In the psychological model for understanding the Trinity you see the God as personal and loving and you see Christian ontological view at work, the mind is absolutely simple yet truly manifold at the same time.  Where does reality lie?  In the whole or the pieces?  The answer is, “reality lies everywhere.”


Thus far in the treatise we have discussed the inadequacy of language as an absolute for understanding God.   We hinted at the role our perceived “perfect language”, mathematics, in society before we shifted our study to Ontology.  We began with the general question of the “one and the many” that causes the conflict in ontological study. We then asserted the Christian view of ontology, that reality is simple and manifold at the same time, that both objects and relationships are equally real.  We were careful to note that asis the case with any ontological view, it is impossible to “prove”.  

In this second section we applied Christian ontology to trinitarian theology by exploring an analogy which displays the Father and the Son as objects and the Spirit as the Loving relationship.  We wrapped up this first section with an extended analogical example that employed a psychological model for the Trinity in an effort to give the reader an exercise which offers phenomenological and experiential knowledge of Christian ontology that is easily relatable in the believer's mind to the Trinity.   

In the next section we will apply our current ontological exploration and trinitarian understanding to mathematics and explore the mathematical formula by which one can teach trinitarian theology. We will learn that our problem has never been math, but ontology, God is fundamental to reality and reality is fundamental to math.  Knowing this eases our discomfort with the dogma of the Trinity which spring from our assumption that math is fundamental to reality and reality is fundamental to God.

  The final section will be a survey of how Christian ontology, which is properly developed from the dogma of the Trinity, expresses itself in other deep mysteries of Christianity.  In this section we will make a cursory study of God as immanent and transcended to creation, Christology, and ecclesiology.  

     


Exploring the Mathematical Formula by Which One May Teach Trinitarian Theology


Previously we laid a philosophical and theological groundwork for understanding the mathematical formula by which one can teach trinitarian theology by distinguishing atomism from monism and then defining Christian ontology as the recognition that reality is simple and manifold at the same time.  We began to see that in a Christian understanding  God is fundamental to reality and reality is fundamental to math.  In the last section we will go to use this information to explore other Christian mysteries such as immanence and transcendence, christology and ecclesiology.  But before that we will pause to use that knowledge to illuminate how one can use math to teach trinitarian theology. 


A Bad Trinitarian Formula

   

One thing that I hope the reader is starting to see is that the “problems” of trinitarian theology are not mathematical. One of the immediate walls encountered when discussing this dogma is the mathematical one because we see math as fundamental to reality and reality as fundamental to God.  However it may be that there is no mathematical dilemma. One need only to look at equations a little differently and it all makes sense.  The common conception of the formula is 1+1+1=1.  This obviously does not make sense mathematically and is not the formula for teaching trinitarian theology.   Before exploring the formula we may need to explore mathematics as such.  

Math is a language.  It is as real and illusory as any other language.  It is one of the more precise languages we have, given that it can be spoken as a completely self referential language and when this is done the language is absolutely tautologous.  By itself it makes complete sense, but when we say that reality is fundamental to math, what we mean is when math is applied to reality we have a much more murky affair.  It is not as easy as one might suspect to look at an object and say “One” and be 100% correct.  Just correct in a way.  Despite the current trend in the hard sciences, math is not the fundamental interpreter of reality, it is simply one useful tool.  Now as we begin to delve into the math it is important to reiterate that we are using analogous language, not providing explanation. The reader will notice we do not offer the mathematical formula that “explains” the Trinity. It is the mathematical formula “by which one may teaches trinitarian theology”.  No linguistic formula can “explain” God.  In fact, to this point what we have demonstrated is that no linguistic formula, including formulas in the language of mathematics, can perfectly explain any aspect of reality.  Now our discomfort with the dogma of the Trinity should suit our discomfort of the entirety of creation, which we must now approach as a great mystery.


Math and Ontology

  

So here is a formula that is of better use for teaching trinitarian theology: 1+1=2.  All  one needs to do is look at the formula like an absolute mathematical idiot and try to make sense of it while aware that reality is fundamental to math, not vice versa.  One sees an equal sign,  that means the things on each side mean the same or are symbolic of the same thing.  Next what one sees is a formula with three things on one side of an equal sign and one thing on the other.  Three is the same as one.  That formula seems to be saying the same thing the dogma of the Trinity is. One may decry this as some sort of category mistake or misunderstanding of math.  Not so, it is a different understanding of math.  In this understanding, math is a language that seeks to describe reality just like any other and the symbols attempt to correspond to things in reality.  To get flustered with this is usually the result of a pythagorean philosophy that sees math as the fundamental interpreter of reality and possibly having an ontological status apart from phenomenological reality itself.  But as Christians, God who is three persons and one God is our fundamental definer of reality.  And math is a constructed language that serves our limited understanding of reality.   

Back to our formula; 1+1=2.  On the left side you see the most basic interpretation, two objects and a relationship.  There are two symbols that denote objects, and there is a symbol that denotes a relationship.  On the other side you have a symbol that indicates the sort of togetherness of those three as a true unit “2”.  To use math to teach the Trinity one must not apply math to reality, but apply reality to math.  Reality is the primary of the two.  We can apply our former ontological inquiry in order to illustrate correct and incorrect understandings of reality.    

An atomist would look at the formula and say 1+1 is the “truer” half of the equation,  because the plus sign is symbolic of the relationship between the two objects, but the objects are the reality the relationship is illusory and symbolized the symbol +.  The monist would look at the equation and point to the 2 as the truer half of the equation.  It is symbolic of the absolute unity of whatever is being indicated.  The other side, 1+1, is indicative of an illusion.  On that side the + sign shows the reality but the 1 and the other 1 are demonstrating an illusion of division in the oneness of reality.  

One invested with a Christian ontological worldview must point to the equal sign and say, this is where reality lays.  Things can be simple and manifold at the same time.   All this, or any other  equation is doing is demonstrating two different ways of saying the same thing, simplicity and diversity are the same.  In fact, all of basic math (addition subtraction multiplication and division) is one large system of showing how diversity and simplicity interact together, all plodding along with equal signs as a constant reminder of the truth.


Figure 5- Doing the Math.jpg

Now this isn’t perfect, no analogy is.  If it were it wouldn’t be an analogy, something similar but fundamentally different.  There are many good analogies that indicate the ontology behind the Trinity and some that are not so good.  The shamrock indicated is a pretty good one, three leaves one plant, the cord of music is another three notes one cord. 

A very popular analogy these days is the water as solid/ liquid/ gas, but as you can see, this is one of the less good analogies.  H2O is not all three at the same time.  “I am a father, son and husband” similarly falls short, those are roles I play with different people and not truly distinct persons abiding within me and present to all people.  But what you get with any analogy is an attempt to show that what is indicated by the Trinity is not foreign or strange, but fundamental to reality, because God is fundamental to reality. 


This section is purposefully short.  It is paramount that the reader see that math is not in contradiction to trinitarian theology, but supplemental to it.  Therefore after exploring more fundamental things, ontology and trinitarian theology, we were able to revise our understanding of the primacy of math.  Once one begins to see that math is a language like an other, useful but imperfect, one can see that it functions as well as any other language at teaching the Trinity, which is to say it is inadequate.  In the last section we will revisit Christian ontology and apply it to some other foundational Christian mysteries, the immanence and transcendence of God, christology and ecclesiology.       



Christian Ontology: Immanence and Transcendence, Christology, and Ecclesiology


In the first section we explored how language is inadequate when trying to describe the nature of God.  From there we discussed the nature of Christian ontology, which asserts that objects and relationships are equally real. 

Following that we applied Christian ontology to trinitarian theology and come to a basic comfort level with the dogma of the Trinity.  We expounded an analogy of God as object, object relationship, which developed into the definition, “God is Love”.  We ended with a cognitive meditation that allows the reader to experience Christian ontology phenomenologically and thereby come to an experience of the trinitarian image and likeness of God within themselves.   

After this we will apply our ontological exploration to mathematics and we defined mathematical formula by which one can teach trinitarian theology, 1+1=2.  If one is investe with a Christian ontological view, this formula demonstrates equality between three “things” on one side and one “thing” on the other.  We learned that our problem has never been math, but ontology, God is fundamental to reality and reality is fundamental to math.  

  In this final section will be a survey of how Christian ontology, which is properly developed from the dogma of the Trinity, and expresses itself in other deep mysteries of Christianity.  In this section we will make a cursory study of God as immanent and transcended to creation, Christology, and ecclesiology.  


Christian Ontology of Immanence and Transcendence


Many of the Christian mysteries revolve around this basic mystery of reality, that things can be simple and manifold at the same time.  So for example, Christians talk about God as immanent and transcendent to creation.  We certainly see God as absolutely distinct and beyond creation in every way.  Yet at the same time God abides in creation and is deeply integrated in every aspect of his creation.  This view is what gives Christians the ability to have a sacramental cosmology, that one can come to the transcendent God through physical reality, such as bread, wine, water, or a human body (Jesus).  This seemingly contradictory set of beliefs is possible because God and creation form a simple but manyfold relationship.  The other abrahamic faiths posit Gd as absolutely transcendent tending to be more atomistic.  This presents Anselm’s problem to the believer.  If God is absolutely transcendent, and creation is absolutely separate then we have a new perplexing formula to ponder, G+C > G; God plus creation is greater than God, and nothing can be greater than God.  On the other end of the ontological spectrum, you have eastern religions, which collapse into pantheism and the very concept of “God” is reduced to nonexistence.      

You can make sense of the Christian dynamic between God and creation by remembering that God’s Spirit proceeds reciprocally between the Father and the Son making them one, but that same Spirit also extends to Creation.  Relationships like Love, which is what The Spirit is, are not bound by space or time, but ever flowing.  As true as the relationship is, this is how true the oneness is but at the same time love does not destroy individuality.  God absolutely loves the entirety of his creation, and is therefore one with it, though truly distinct.    

Our Christian narrative points out that there is a problem here.  Love must be reciprocal to be perfect just like being a part of a plant does not stop a leaf from being a leaf.  Given this unity it is important to remember that though God does perfectly love us we do not perfectly love Him.  This is sin, the absence of that Love and the resulting alienation.


Christian Ontology and Christology  


Once again, with our Christian ontological view that Jesus is a human and the unique God is not as impossible to conceive as it was thought without the Christian ontological lens.  The Son of God, who is distinct from the Father but in the unity of the Holy Spirit is one with the Father, is from the beginning of his conception one with the human nature of Jesus of Nazareth in the union of perfect love that is the Spirit.  These two natures are truly distinct, and actually have two distinct wills. But, the human will is completely subservient to the divine out of love making them act as one. With this knowledge you can hear Jesus say in John’s gospel I and the Father are one, but four chapters later say the Father is greater than I, and it makes sense, not in a switch hitting way where human Jesus is saying one and divine Jesus is saying the other, but because they are simultaneously true.  


Figure 6- Two Natures of Christ.jpg

Christian Ontology and Ecclesiology


As part of Christ’s mission he founds The Church, a group of people who are one and bound to him as his mystical body. With the Holy Spirit sent out after the ascension The Church is established as one with Christ and yet distinct from him, bound by the relationship of Love.  This is a collective reality for its members, but works on the individual level as well.  Each of us is bound to The Church as a whole and through that bond to Christ, in the Love we experience.  The preceding sentence is absolutely non-controversial, but interpreted with a Christian ontological view the depth of the bond is understood as more profound the more the loving relationship is present up to the point of being absolute oneness in a perfectly loving relationship.  Since relationships are as real as objects, what you have in the end is an entire system that is completely manifold and absolutely simple at the same time. Every level is truly distinct and all are truly one.  So in Sunday school, when the good sister says, “In heaven you’ll be one with God.”  And the nervous child says, “But will I still be me?” and the good sister says, “Yes!”  This isn’t simple indoctrination of contrary facts.  It is an attempt to instill a different way of looking at the basic way the world works.  What you have at the end is a “cloud of witnesses”  a Cloud being one simple reality, that is part of the sky, but composed of the innumerable droplets that anyone who has walked through a fog bank has experienced.

 


The concepts up to the present point will be extremely helpful if the reader were to review the concept of sacral sex as noted in the treatises Birth Control vs Labor Rights? and Corporeal Unitive Fulfillment in the Eschaton.  In a sacramental marriage the husband and wife truly become one in an inseparable way and the grace present there brings the participants into a state of sanctification and oneness with God.  The understanding of how grace and physical reality connect, the understanding of reality as simple and manifold at the same time are no longer assumed by the majority of Christians.  Unfortunately that means they must be learned, giving them the character of esoteric knowledge instead of lived experience.  But the more one can immerse oneself in these world views the better one will be able to live a deeply Christian life.  Thankfully, though culture does not necessarily reinforce these assumptions, as individuals and small Christian communities we can live them personally and come to know them in all their profundity.  


Conclusion


In this treatise we have attempted to make the dogma of the Trinity comfortable to the believing Christian.  We began by making the believer uncomfortable with the entirety of creation by  showing the inadequacy of language in general when speaking of God, and then review two basic ontological positions, atomism and monism, and demonstrating how each of them is inadequate.  At this point we know nothing of God or creation.  We then explored Christian ontology, which asserts that reality is simple and manifold at the same time and believes that objects and relationships are equally “real”.  This was shown to by example to be the common experience we have of reality and therefore not a unique or uncommon aspect of God. 

After that we gave a brief survey of the persons of the Trinity and how by relation to each other they form one reality.  From there we explored how basic mathematics is simply a massive language set that, by means of the equal sign, seeks to demonstrate that reality is simple and manifold at the same time.  We explored the mathematical formula by which one may teach trinitarian theology, 1+1=2.  We showed how it demonstrates that three “things” (object, relationship, object) are equal to one “thing” (their sum).  We then analogously applied this to the Trinity. A lastly we briefly applied Christian ontology to other great mysteries of The Church, the immanence and transcendence of God, christology, and ecclesiology.  We did not “solve the problems, of these fields, we simply made them accessible to the rest of reality by a systematic overview of Christian ontology.            


In conclusion we now return to our muslim missionary who asserted confidently to us that God is one and dared us to mention the Trinity.  His confidence is based on his belief that math is primary to both reality and to God, even though a muslim should know better.  Our reaction should not be to despair at the complexity of our dogma and cower before attempted explanation.  Nor should our response be to enter a contest revolving around whose religion makes the most ridiculous belief claims in order to test the faith of its adherents.

Combatively we may say, “then God added to creation is greater than God and you have a theological problem on your hand a al Anselm of Canterbury.” But instead our simple answer is to assert that we believe God is one as well.  Yet we also understand that reality is not as simple as math and certainly neither is God.  Reality is one, yet reality is also infinitely manifold.  Reality gets this characteristic from it’s creator, who is the fundamental demonstration of Christian ontology, simple and manifold at the same time, one God three persons.  The conclusion of one’s preamble would be, Name anything that is “one thing”? And let the philosophical sport begin.              

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