Something exists.

(This is a properly basic belief. It needs no proof or evidence)

 

Whatever exists, it is itself.

A=A, G=G, etc.

This is the Axiom of Identity. The most fundamental and basic axiom of logic.

This fact is universally and fundamentally true. It must necessarily exist.

Represent the Axiom of Identity as ★

 

What can it do? It can't go anywhere (because we haven't yet defined any kind of space or time). The one thing Existence can do is exist.

 

Existence exists.

(This statement is a self-referential tautology; a recursive fact pointing back to itself.)

We’ll use G for this since we're talking about the basis or Ground of all existence (also G for God).

G=G

 

What are the properties of the Ground of all existence (G)?

Obviously, it must exist, and it must be itself (the identity axiom ★). 

 

In order to construct the Identity Axiom, we needed to relate G to G using the equals sign. So we needed to assume some kind of logic. So we conclude:

 

Logic exists.

(The statement “logic exists” is logically necessary)

 

Since G  is all that exists, it can only exist in relation to itself.

 

So we'll define G using Set Theory:

G = {★, L, G}

 

G has 3 things:

 

★ = The Identity Axiom (“I AM that I AM”)

L = Logic (the eternal Logos)

G = The fact that Existence exists in relationship with itself, within itself, and containing itself (“The Word was with God and the Word was God”=mutual indwelling=perichoresis=the loving flow between Father and Son=the activity and life of God who is also God Himself=the Spirit)

 

The rules of standard set theory don't usually let you have sets that contain themselves, but there's nothing illogical about it. For example, you can have a Google Drive link that takes you to a folder that contains that same document with the link. This is called a Hyperset, and it only works for cases of total self-reference¹. The logic is circular, but I say, if anything is allowed to have a circular definition, it's the identity axiom (G=G). 

 

We could also imagine ★ as the Source of existence. When it radiates a pulse of its existence, we could consider that as being its Signal. Since Signal can only exist in relation to Source, Signal returns to Source in an eternal loop. 

(In Linear Logic used in computation, the ★ is seen as a pulse in a wire or a token traveling around. That doesn't exactly apply in this case, but thinking of it this way lets us describe things using the tools of Linear Logic²).

 

If you imagine ★ as a token of existence pulsing, you can count those pulses: 1, 2, 3…

If you imagine a pulse from Source to Signal as a positive number, you can imagine the return pulses as negative numbers. Continue applying that idea, and you get the rest of math.

Math is the logical expression of existence. Or Existence + Logic = numbers.

 

Another way to say that is that Existence exists infinitely, but if you filter infinity through logic, you get all the finite subsets of infinity (i.e. all numbers).

 

Conclusion:

Existence, logically, must exist

Existence is an eternal fact.

Ultimate reality is existence expressing itself to itself. 

Existence expressing its existence through logic generates a directional flow from the source of existence (Source), through the logic of existence (Signal), and back to the Source.

Math is existence expressed through logic.

 

This is the logical and mathematically consistent way of communicating historic theological ideas such as:

The Father, Son, and Spirit are each fully God, but there is only one God

The Father is not the Son, the Son is not the Father, etc…

The Father begets the Son

The Father is the source of life

The Father has a Word (i.e., the Father can think and speak)

The Father can hear what He Himself says and understand what He Himself thinks

The Son is the radiance of the glory of God and the exact representation of his nature/character 

The Father, Son, and Spirit are eternally “in” one another

Etc.