A Mathematical Proof for the Existence of the One God

Vivificat - From Contemplation to Action ^ | 5 May 2015 | ن Teófilo de Jesús ن (@vivificat)

[Teófilo]

Brothers and Sisters: Peace be with you.

Frequently, Internet atheistic aces challenge me to provide evidence and/or proof for the existence of God. Almost all the time the proof they demand is, on its face, absurd because it is empirical in way or the other and God, if they only knew what the word "God" is, lies beyond any empirical proof. No matter, they keep insisting and the silence of the impossible experiment is proof enough for them.

This post is not address to those narrow, sterile minds because they've closed themselves within and become impermeable to any argument. Their minds already closed to reason present an insurmountable obstacle to sober argument. The only thing left to do for them is to pray.

Instead, this proof, proposed  by the mathematician Kurt Gödel (1906–1978), is a mathematical expression of the ontological proof proposed by St. Anselm of Canterbury (1033–1109) and should appeal to the open-minded and logic-bound. Now, St. Anselm's argument goes like this:

God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist.

It is an argument that really bothers people and has been persistently attacked ever since, yet it keeps surfacing.

The Proof

Gödel utilized modal logic and distinguished between necessary truths and contingent truths.It goes like this:

• Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
• Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
• Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified

• Axiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positive
• Axiom 2: A property is positive if and only if its negation is not positive
• Axiom 3: The property of being God-like is positive
• Axiom 4: If a property is positive, then it is necessarily positive
• Axiom 5: Necessary existence is a positive property

Axiom 4 assumes that it is possible to single out positive properties from among all properties. Gödel comments that "Positive means positive in the moral aesthetic sense (independently of the accidental structure of the world)... It may also mean pure attribution as opposed to privation (or containing privation)." (Gödel 1995). Axioms 1, 2 and 3 can be summarized by saying that positive properties form a principal ultrafilter.
From these axioms and definitions and a few other axioms from modal logic, the following theorems can be proved:

• Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
• Theorem 2: The property of being God-like is consistent.
• Theorem 3: If something is God-like, then the property of being God-like is an essence of that thing.
• Theorem 4: Necessarily, the property of being God-like is exemplified.

Symbolically, it looks like this:

Now, in English

This is my blurb understanding of this proof in English:

If you understood what is meant by "God" you will instantly understand that he cannot not exist; God; objective, concrete existence is a mandatory predicate of the being "God".

Limitations

We need to be careful and hones regarding what this proof does and does not do. It would be intellectually dishonest to ascribe to Gödel's proof claims it doesn't make.

1. It does not prove the Triune nature of God as we Christians see Him;

2. It does not prove a Theistic (i.e. Christian, Jewish, or Islamic conceptions of God) conception of God; "God" can still be conceived in Deistic terms;

3. It makes no moral claims; it attaches no specific ethic or moral demands from God toward rational creatures.

4. It doesn't do away with panentheism ("'God' is in everything, but not everything is 'God'" type of belief)

5. It doesn't establish that the one God created the universe out of nothing.

What it does

What does Gödel's proof actually accomplishes?

1. It does away with theoretical atheism - the one embraced and screamed by today's "New Atheists".  Atheist is proved to be an abstraction and not an accurate description of objective reality; the affirmation "There is No God" becomes meaningless in the real world, but perhaps meaningful in fictitious or imaginary worlds, confined there along with unicorns and the Flying Spaghetti Monster..

2. It rules out polytheism - belief in many gods.

3. It rules out  pantheism.

In the end...

Look, for reasons I explained above, Gödel's elaboration of St. Anselm's ontological proof will mollify Internet atheists. They will keep living as if God didn't exist, as dwarf versions of Nietzsche's supermen. They will live thus because that's what how they wish to live and admitting the existence of God would be inconvenient. They will go on demanding their empirical evidence without even bothering to understand why, when it comes to God, such evidence can't be had.

Of course, if they would bring themselves to understand what "God" is in the hierarchy of beings, they would understand why, and they would stumble open St. Anselm's and Gödel's proof and start the circle of affirmation and denial again, without bothering to think.

Now for us Christians, Gödel and St. Anselm created a threshold or vestibule to a temple inside which, in its sanctuary, we may find the one God and, in its Holy of Holies, we find God revealed in Jesus Christ.

The Holy of Holies is open for all of us. We must decide if we walk from the lobby into the sanctuary and then, into the Holy of Holies to meet Him in Person. He calls us to Himself, in fact. Will we heed His voice?

Future considerations

I think it might be possible to use this proof as a starting point for expressing St. Thomas Aquinas Five Arguments for the Existence of God, utilizing modal logic . However, that's beyond my capabilities for the moment. Perhaps some of you could do it? 

Source of Gödel's proof: Wikipedia.

[Zeneta]

His conception cannot be labeled or captured in any finite set of symbols that fully describes Him.

The "Artist formerly known as Prince"

All kidding aside.

I actually understood some of what you posted.

If I may.

The fact that we "know" there are things we can't "Know" given the limitations of our "logical systems" AND what we do "Know" is wholly incomplete. Therefore, we can't use "Logic" as we know it, to explain everything.

[Heart-Rest]

"Well, the math certainly appears to be in order. "

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Yes it does (and I double-checked it on my calculator before the battery went dead).

[ForYourChildren]

“The fact that we “know” there are things we can’t “Know” given the limitations of our “logical systems” AND what we do “Know” is wholly incomplete. Therefore, we can’t use “Logic” as we know it, to explain everything.”

Yes, and there are some mathematical proofs that prove that we will never be able to prove a specific conjecture.

So, coupled with Godels general incompleteness theorem. We have theorems which can be proved, theorems which can’t be proved, theorems that prove some theorems cant be proved, so are there theorems that prove that there are not theorems to prove some theorems, etc. etc......

[Heartlander]

Thanks - you might also like Tim Keller
(Note: These are sermons based on his book - this is not the actual book, which I highly recommend)

The Reason for God MP3s by Tim Keller

Direct links to the audio files are below, or use the RSS Feed here.

• Exclusivity: How can there be just one true religion? MP3
• Suffering: If God is good, why is there so much evil in the world? MP3
• Absolutism: Don't we all have to find truth for ourselves? MP3
• Injustice: Hasn't Christianity been an instrument for oppression? MP3
• Hell: Isn't the God of Christianity an angry Judge? MP3
• Doubt: What should I do with my doubts? MP3
• Literalism: Isn't the Bible historically unreliable and regressive? MP3

[Zeneta]

Yes, and there are some mathematical proofs that prove that we will never be able to prove a specific conjecture.

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Incompleteness to say the least.

Yet, the default position among the secularist’s is to say, “just because we don’t know NOW, doesn’t mean we won’t ever know”. “That is science, after all”.

In the meantime, just accept what we do know even though it may be revised as we go along. No reason to fall into some “Faith system”.

Nevermind that in order to satisfy the real challenges they face, they have invoked any number of “theories” that are unprovable. Multi-worlds, Multi-Verse and any number of “alternate Reality” scenarios.

Why is it called “DARK MATTER”? or “DARK ENERGY”?

Because they have absolutely no CLUE.

[annalex]

If God exists in the understanding, we could imagine Him to be greater by existing in reality.

...Therefore He also exists in reality. Therefore He exists in the full sense. Good article. I'll index it on my profile for future reference. Thank you.

[St_Thomas_Aquinas]

Is math abstract?

Yes.

Numbers and equations are universal concepts (Universals) that only exist in minds, except for one[ness], or unity, which is an essential characteristic of each and every individual thing.

We know that number does not inhere in individual things, because the same object can be considered to be 1 of 5 or 2 or 12, etc.

The (universal) concepts themselves (like "5") are not observable or measurable.

These universal concepts have been found to conform to external realities, and are believed by most people to be true regardless of time or place.

Since concepts exist in minds, eternal, universal concepts would have to be grounded in an eternal Mind.

[Teófilo]

Clearly, we’re not talking about the certainty that comes from faith as infused by the Holy Spirit. That involves another set of distinct operations and consequences.

This is an exercise on how the natural mind, without the assistance of faith, can reason out the existence of God.

~Theo