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.

[Teófilo]

This is great, but difficult to reconcile with quantum mechanics as I (poorly) understand it.

~Theo

[Teófilo]

I am fan, and a frequent user of Pascal’s Wager. A great argument indeed. Hated by unbelievers though, because even not choosing is a choice and they often take umbrage under not choosing.

~Theo

[Heartlander]

Video

[afraidfortherepublic]

Faith rules. Mathematics, not so much!

[ETL]

Einstein was a follower of the static universe theory until Hubble came along and proved Lematre to be correct.

Einstein created his famous fudge factor cosmological constant around that time. Because, according to his general relativity theory, the universe should be collapsing under gravity. Since the observations showed it wasn't, but rather, instead, expanding, he doctored his equations to fit the observations. He called the constant, the "biggest blunder" of his life. Decades later, it was shown that, not only was the universe expanding, it was accelerating due to some still mysterious force or other mechanism. As it turned out, Einstein was right, but for the wrong reason.

[Sergio]

bkmk

[Teófilo]

For some, math is the threshold of faith. For others, is the beginning of hell... :-D

~Theo

[afraidfortherepublic]

Count me in the latter category!

[AllAmericanGirl44]

Bkmk

[bjorn14]

This is all very quaint but are belief in God comes not from reason but the wooing of the Holy Spirit.

Althought I have seen the quote “Math is the language God created the universe with.” I am sticking with Jesus’ words “Blessed are those who have not seen and believed”

[JoeFromSidney]

I've never been happy with Anselm's proof. As someone has put it, you can almost see the rabbit being put in the hat. If people will accept it, I won't argue with them. However, I prefer Aquinas's proofs.

[mlo]

I was addressing the proof. However, making excuses for not needing evidence is not “thinking hard”.

[Zeneta]

I really enjoyed the video you posted.

Thanks.

I’ve come to like using “Presuppositional Apologetics” when addressing some people.

I particularly like the work from Dr. Jason Lisle.

This is a short example from a much longer presentation.

“Without God There Could Be No Logic (Dr Jason Lisle)”

https://www.youtube.com/watch?v=2aLYIu4SoFE&index=5&list=PLcVH49JPp7UV7FqThLicwDeuTlcF_EKWy

[Verginius Rufus]

"Oh, that was easy," says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing."

You have to watch out for those zebras. They look so harmless.

[windcliff]

ping

[St_Thomas_Aquinas]

Mine's shorter.

Math exists.

Therefore, God exists.

[jaz.357]

The one and Only?

[Zeneta]

Math exists.

Therefore, God exists

---

Is math abstract?

[Gideon7]

"I get it. You don't want us cycling between a ladder and a chute for eternity."

"Ack! It's 'forever', not 'eternity'! Get it right! You know how much that annoys me when you mix those up."

"Sorry. Uh, I forgot. What is the difference between forever and eternity again?"

"Look, I told you a dozen times! Forever is in principle algorithmic. Eternity isn't."

"Oh yeah.. I forget what that means.."

"Keiichi, I already explained this. I swear, the high altitude must be making you stupid or something. Okay, let's go over it again. Forever is in principle algorithmic. It means that there exists, at least in theory, some kind of generating function or description for it. For example, you can express the set of factorials of all non-negative integers like this, written in the functional computer language Haskell:

fac 0 = 1
fac n = n * fac (n - 1)

"The set of factorials is infinite, but there exists a well-formed algorithm that describes how to generate them. A more complex example is the set of prime numbers. For example, here is a function to generate an arbitrarily long list of prime numbers, also written in Haskell:

primesTo m = 2 : sieve [2..]
where
sieve (p:xs) = p : sieve [x | x - xs, rem x p /= 0]

"Now, there is no easy way to predict whether any given really big number happens to be in this set. In fact, it is the hardness of the factorization of large numbers that is the foundation for the computer encryption algorithms that you find on the World Wide Web [SSL and TLS]. When you purchase something from Amazon with your credit card, or when you transfer money from your Fidelity bank account, your computer is actually using the factorization of a large number into two large primes to encrypt your account information.

"So now let us move up to a more abstract level. Let's define the set S of all Haskell programs that return the answer '1'. Here is the question: Is there a generating function for S that can be described using Haskell itself? In other words, can you write an algorithm written in Haskell, like the ones shown above, that will generate the set of all such Haskell programs?

"The answer is no. In the lingo of computability theory, it is undecidable. According to Gödel you could say that the Haskell programming language is 'incomplete', in the sense that it cannot express all expressible truth statements (members of S) within that logical system. So it is 'imperfect' in that sense. Yeah, I know this is easily provable using the Halting Problem, but bear with me here. The point is, any such sufficiently complex system that can be described using finite symbology is by necessity either incomplete or inconsistent. That is a direct consequence of Gödel's Incompleteness Theorem: That no such logical system can be both completely consistent (internally perfect) and can find and prove all its truth statements within that system (is complete). Such a system cannot possibly exist."

Keiichi said, "In other words, it is flawed."

"Yeah. Now let us move up to a really ambitious logical system. Remember when I described to you the Standard Model of particle physics, the so-called 'Theory of Everything'? The TOE?"

"Uh, yeah.."

"If you recall, the Standard Model describes the dynamical behavior of the fundamental particles of the physical universe within a quantum mechanical system whose gauge symmetry can be expressed as a function of the Lagrangian, L."

"In other words, it's a model. A system."

"Yes. And so in principle it can be generated algorithmically, although as a practical matter that's actually infeasible."

"Okay."

"So now, here is the big question: Is this model perfect? In the Gödelian sense?"

"It's a finite description, so no, it is not."

"Correct. So could you conclude that, in that sense, that the design of the physical universe is flawed?"

"Sure. In the sense that the quantum states are based on the operation of that finite TOE model. Okay, fine. But I still don't see what you are driving at."

"Don't you see, Keiichi? One of the big arguments against the existence of God is that His creation is flawed. God is perfect, the argument goes, but his creation is imperfect. Creation is messed up. And so atheists claim that this apparent contradiction refutes the existence of perfect God."

"Ah, I see. But we just established that a perfect creation is impossible to create."

"Bingo! Yay! I love it when you get clever." She playfully approached him to tousle his hair, but he jumped back before she could do it.

"Hey, don't muss up my hair! You know I hate that."

"Feh, like your hair can get any more mussed up than it already is. You never comb it."

"Just don't touch it. Anyway, I think I get what you are saying."

"The point is, God's creation is flawed by necessity. It is not His fault, it just is. By logical necessity. It is intrinsically flawed due to its nature of being described by finite rules."

"Got it."

"Now let's get really ambitious. God is perfect. So tell me, Keiichi, how would you describe God then?"

"You can't."

"And why not?"

"Uhm.."

"Before you answer, think carefully about the little thought experiment that we just did."

Keiichi thought hard. "Hmm.. the nature of God cannot be described by any finite logical system."

"Hooray! You got it! You win a kewpie doll! This is what we mean when we say God is eternal."

"In other words, God is literally indescribable."

"Correct. When we call something 'eternal', what we mean is that it cannot be described in finite symbols. Now you are ready to understand the distinction between 'forever' and 'eternal'. An entity that is eternal is something that cannot be conceived using finite terms. This is why Gödel cannot capture God within his nasty logic trap. Because to capture Him that way Gödel needs to first come up with a symbol that fully describes Him, and there isn't one.

"Is that why Jews are so reluctant speak God's name aloud?"

"I like to think so. You see, in a certain sense one can argue that God has no name. For he literally cannot be named by any symbol. More specifically, His conception cannot be labeled or captured in any finite set of symbols that fully describes Him."

Keiichi said, "I am rather amazed that I actually understood that."

"Heh, good boy. I admit these are rather deep concepts, but I think they are important."

"Is that what we are approaching as we climb up?"

"Yeah, I think so. I have a sneaking suspicion that the place where Big Sis dwells is actually eternal."

"Wow.."

---

[ Excerpt from After Ragnarok, Chapter 37. ]

[St_Thomas_Aquinas]

For some, math is the threshold of faith. For others, is the beginning of hell... :-D

LOLZ The whole family liked that one. 8-)