Correct Trinitarian formula?

I’m trying to better understand how Trinitarians describe the Trinity. In other threads LW7 and SteveVH have graciously offered explanations to my inquiries. One concise definition seems to be that The Father is God, the Son is God, and the Father is not the Son. Am I correct?

Mathematically, this seems to say “A equals B, C equals B, and A is not equal to C”.

Does this mathematical equation/representation capture the Trinitarian view of the relationship between the Father and the Son? Thanks in advance.

DId you mean B is not equal to C or A is not equal to C? Your equation does not seem to follow your text.

First, you can’t expect to diagram or reduce to finite mathematics an infinite concept. But that aside, the fact that the Father is not the Son does not mean they are not equal. Both are God.

Theology using Math? Lol - hmm, I think it would be more acurate this way:

A = B&C, B=C&A, C=A&B in that each Person in the Trinity is God, One God
A is Not B or C, B is Not C or A, C is Not A or B in that no Person of the Trinity is the same Person as another Person in the Trinity, the Father is Not the Son - only the Son is the Son for example

Don’t forget 1 + 1 + 1 = 1 :smiley:

I think it’s best not to reduce the Trinity to mathematics (I’ve seen some say something like 1x1x1=1 :rolleyes:).

Quite simply:

The Father is God
The Son is God
The Holy Spirit is God

The Father is not the Son nor the Holy Spirit
The Son is not the Father nor the Holy Spirit
The Holy Spirit is not the Father nor the Son

They are three distinct Persons, who are not each other, and are one God. Put another way, the one God, the “being” of God, eternally exists as three distinct Persons, Father, Son, and Holy Ghost.

Here is some of what the Catechism of the Catholic Church states:
253 The Trinity is One. We do not confess three Gods, but one God in three persons, the “consubstantial Trinity”.83 The divine persons do not share the one divinity among themselves but each of them is God whole and entire: "The Father is that which the Son is, the Son that which the Father is, the Father and the Son that which the Holy Spirit is, i.e. by nature one God."84 In the words of the Fourth Lateran Council (1215), "Each of the persons is that supreme reality, viz., the divine substance, essence or nature."85

254 The divine persons are really distinct from one another. "God is one but not solitary."86 “Father”, “Son”, “Holy Spirit” are not simply names designating modalities of the divine being, for they are really distinct from one another: "He is not the Father who is the Son, nor is the Son he who is the Father, nor is the Holy Spirit he who is the Father or the Son."87 They are distinct from one another in their relations of origin: "It is the Father who generates, the Son who is begotten, and the Holy Spirit who proceeds."88 The divine Unity is Triune.

255 The divine persons are relative to one another. Because it does not divide the divine unity, the real distinction of the persons from one another resides solely in the relationships which relate them to one another: "In the relational names of the persons the Father is related to the Son, the Son to the Father, and the Holy Spirit to both. While they are called three persons in view of their relations, we believe in one nature or substance."89 Indeed "everything (in them) is one where there is no opposition of relationship."90 "Because of that unity the Father is wholly in the Son and wholly in the Holy Spirit; the Son is wholly in the Father and wholly in the Holy Spirit; the Holy Spirit is wholly in the Father and wholly in the Son."91 *

I think the Athanasian Creed sums it up :thumbsup:

The Athanasian Creed

Written against the Arians.

Whosoever will be saved, before all things it is necessary that he hold the catholic faith. Which faith except every one do keep whole and undefiled, without doubt he shall perish everlastingly.

And the catholic faith is this, that we worship one God in Trinity, and Trinity in Unity; Neither confounding the Persons, nor dividing the Substance. For there is one Person of the Father, another of the Son, and another of the Holy Ghost. But the Godhead of the Father, of the Son, and of the Holy Ghost is all one: the glory equal, the majesty coeternal. Such as the Father is, such is the Son, and such is the Holy Ghost. The Father uncreated, the Son uncreated, and the Holy Ghost uncreated. The Father incomprehensible, the Son incomprehensible, and the Holy Ghost incomprehensible. The Father eternal, the Son eternal, and the Holy Ghost eternal. And yet they are not three Eternals, but one Eternal. As there are not three Uncreated nor three Incomprehensibles, but one Uncreated and one Incomprehensible. So likewise the Father is almighty, the Son almighty, and the Holy Ghost almighty. And yet they are not three Almighties, but one Almighty. So the Father is God, the Son is God, and the Holy Ghost is God. And yet they are not three Gods, but one God. So likewise the Father is Lord, the Son Lord, and the Holy Ghost Lord. And yet not three Lords, but one Lord. For like as we are compelled by the Christian verity to acknowledge every Person by Himself to be God and Lord, So are we forbidden by the catholic religion to say, There be three Gods, or three Lords.

The Father is made of none: neither created nor begotten. The Son is of the Father alone; not made, nor created, but begotten. The Holy Ghost is of the Father and of the Son: neither made, nor created, nor begotten, but proceeding. So there is one Father, not three Fathers; one Son, not three Sons; one Holy Ghost, not three Holy Ghosts. And in this Trinity none is before or after other; none is greater or less than another; But the whole three Persons are coeternal together, and coequal: so that in all things, as is aforesaid, the Unity in Trinity and the Trinity in Unity is to be worshiped. He, therefore, that will be saved must thus think of the Trinity.

Furthermore, it is necessary to everlasting salvation that he also believe faithfully the incarnation of our Lord Jesus Christ. For the right faith is, that we believe and confess that our Lord Jesus Christ, the Son of God, is God and Man; God of the Substance of the Father, begotten before the worlds; and Man of the substance of His mother, born in the world; Perfect God and perfect Man, of a reasonable soul and human flesh subsisting. Equal to the Father as touching His Godhead, and inferior to the Father as touching His manhood; Who, although He be God and Man, yet He is not two, but one Christ: One, not by conversion of the Godhead into flesh, but by taking the manhood into God; One altogether; not by confusion of Substance, but by unity of Person. For as the reasonable soul and flesh is one man, so God and Man is one Christ; Who suffered for our salvation; descended into hell, rose again the third day from the dead; He ascended into heaven; He sitteth on the right hand of the Father, God Almighty; from whence He shall come to judge the quick and the dead. At whose coming all men shall rise again with their bodies, and shall give an account of their own works. And they that have done good shall go into life everlasting; and they that have done evil, into everlasting fire.

This is the catholic faith; which except a man believe faithfully and firmly, he cannot be saved.

Three persons

One substance

Three persons each share the same substance

The three persons are each their own individual however wtihin the same substance and are not each other.


A = X

B = X

C = X

C does not equal A or B
A does not equal B or C
B does not equal A or C

Of course explaining how it works is impossible because GOd is beyond us.

Well… when I was teaching this in Sunday School I always used the Athanasian Creed with the previously mentioned “The Father is God… The Holy Spirit is not the Son and is not the Father” formula (usually as a diagram.)

The basic concept is pretty simple: We have one “What” or substance (God) and three “Whos” or persons (Father, Son, and Holy Spirit.) Where I think people get hung up on this is that they want to find an analogy for it and there isn’t one. In nature there is an exact correspondence between persons and substance, but God simply doesn’t work that way and God is the only thing that doesn’t work that way.

At that point, someone would usually say, “Well… that just doesn’t seem right,” and I would then point out all of the other ways in which God is in a category entirely unto Himself: His eternal nature, His self-sufficiency, etc. Leading inevitably to the only “Aha!” moment that any of us can ever really get to with regards to a lot of this stuff. Namely, that there are, ultimately, two categories of everything that is: God and everything else, and that trying to talk about God in everything else’s terms is a category error.

About the only analogy I’ve ever heard that works is C.S. Lewis’ analogy of trying to explain a cube to a two-dimensional person. Even that falls flat (if you’ll pardon the pun), because while a cube is certainly one thing comprised of an arrangement of other things, the other things that comprise the cube are not substantially united. You can slice a square off a cube and it will remain a square, although the cube will cease to be a cube. You can’t slice the Son off of God and still have God… or, for that matter, the Son.

At the end of the day, what we have to do is accept the Trinity because God tells us that that’s how He is and then leave it at that. The Trinity, to use the catholic terminology, is an absolute mystery: It is a truth that is impossible for us to discover on our own and may only be understood partially and then only by analogy.

Thanks everyone for your responses.

A pretty good explanation I’ve heard is the example of using water.

You can have solid, liquid, and gaseous water. They are all water, but they have different individual properties.

Thats akin to modalism. Because the different states are not the other. It cannot be both solid ice and liquid water at the same time. it changes from solid into liquid into steam. Whereas the trinity doctrine would maintain that the father is the father at the same time the son is the son as the spirit is the spirit. There is no changing or shift into different modes.

Hence, why it’s not a perfect analogy, but if there were a perfect analogy to the Trinity, it wouldn’t still be a Mystery, would it?

But yeah, it would be as if you could have water existing as all 3 states at once.

The water analogy is alright for proving the logical point that three in one is not contradictory on its face, but it does nothing to really address the question of how the persons in the Trinity are distinct from one another because while there may be three different forms of water, there are not three “forms” of God. God is the same form as his being.

The terms “being”, (or “substance”) and “person” (or the distinction between the two) are uniquely Christian ideas which developed within the Church in order to better define this great mystery. One however, does not have to even know of or understand the formal definition as long as one accepts the doctrine which is materially present in Scripture, if not formally defined.

A u B u C = A n B n C.

Better example than water is light.

Red union Yellow union Blue is White.

I think we need to forget about formulas altogether. Not only do each of them fall short, they can lead us in the wrong direction. We are seeking to understand the almighty God, the Creator of the universe who is eternally above us in every way. We are seeking to understand a divine Being who is absolutely unique and for whom we have no analogy on this earth. It is enough to accept divine revelation and believe in three divine persons in one God; Father, Son and Holy Spirit.


You cannot add God.
You cannot subtract God.
You cannot multiply God.
You cannot divide God.

But there is union, a relationship which belongs more in the realm of set notation than arithmetic.

One thing that really annoys me is when people take the word “IS” and think it means “=”. The OP converts “The Father is God, the Son is God” into “A equals B, C equals B”.
That is just not a valid application of the word “IS” Its like saying “the sky is blue” therefore “sky equals blue”. And his logical attempt to triumph the Triune, by invalidating the Triune, is to state “sky is blue, lake is blue, sky is not lake”. There is no logical fallacy.

Yes. This properly articulates the logical relationship between the persons and substance of the Trinity.

However, your assumed syllogism is both logically fallacious and not representative of traditional Christology, as it equivocates the persons of the Trinity for the substance thereof. Let’s parse this down a bit:

A: The Father
B: God
A = B: The Father is God

C: The Son
C = B: The Son is God

The way you’ve caricatured the Trinity has it such that the Father and the Son are equivalent (i.e. A = C), yet as you aptly point out the Catholic Church does not teach this (though I’m impressed to think that you believe this ought to be the logical conclusion. Perhaps I’ve misread your OP).

Implicit in all this is a compounded Affirmation of the Consequent (e.g. X → Y; Z → Y; Y ∴ X ⋀ Z). If X then Y; if Z then Y, Y therefore X and Z. Notice that the conclusion (Y therefore X and Z) requires that the only way the ultimate predicate can arise is if its source in any and both premises is assumed.

We know that affirming the consequent is logically fallacious because Y existing doesn’t necessarily mean that X and/or Z gave rise to it.

A more simple form of Affirming the Consequent is: X → Y; Y ∴ X (If X then Y; Y, therefore X).

This makes more sense when we apply an example:

X: Human
Y: Mammal


X → Y: If it is a human, then it is a mammal.
Y: It is a mammal
∴ X: Therefore, it is a human.

Obviously we can think of countless examples of individuals that would qualify as mammals but not humans.

Let’s bring this back to the Trinity. Just because the Father is God, and the Son is (independently) God, doesn’t mean that the Father and the Son are the same person, anymore than saying just because a Human is a mammal and a cat is a mammal, therefore a Human must be a cat!

Does that actually work?

I’m assuming your variables A, B, and C relate to the Father, Son, and Holy Spirit, respectively. Is this correct? If so, then you’re missing a variable: the substance (X?)

All you’ve done here is state that the Father or the Son or the Holy Spirit are the Father and the Son and the Holy Spirit. I’m not yet Catholic, but this doesn’t sound right to me.

Edited to Add:

In other words, it seems to me that you’re saying that any given person of the Trinity is the culmination of all three persons. Isn’t this modalism?

or the Holy Spirit are the Father and the Son and the Holy Spirit. I’m not yet Catholic, but I’ve studied quiet a bit and this doesn’t sound right to me.

Edited to Add:

In other words, it seems to me that you’re saying that any given person of the Trinity is the culmination of all three persons. Isn’t this modalism?

No it is not saying that. It is not modal at all (which I believe is unitarian). A is not B is not C (and they are not variables they are constants). If A is B is C then that is modalism. The substance is the union, but I have forced intersect to prevent the opposite false doctrine.

Ah! I assumed that your use of ‘u’ was to mean ‘⋁’ (the logician’s “or”), rather than Set Theory’s union ‘⋃’.

My bad! :slight_smile:

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