God proof models (1 Viewer)

[magnifier661]

http://en.wikipedia.org/wiki/Gödel's_ontological_proof

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 1 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 2, 3 and 4 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.

http://www.spiegel.de/international...ically-prove-goedel-god-theorem-a-928668.html

Proving God's Existence with a MacBook

That is where Christoph Benzmüller of Berlin's Free University and his colleague, Bruno Woltzenlogel Paleo of the Technical University in Vienna, come in. Using an ordinary MacBook computer, they have shown that Gödel's proof was correct -- at least on a mathematical level -- by way of higher modal logic. Their initial submission on the arXiv.org research article server is called "Formalization, Mechanization and Automation of Gödel's Proof of God's Existence."

The fact that formalizing such complicated theorems can be left to computers opens up all kinds of possibilities, Benzmüller told SPIEGEL ONLINE. "It's totally amazing that from this argument led by Gödel, all this stuff can be proven automatically in a few seconds or even less on a standard notebook," he said.

The name Gödel may not mean much to some, but among scientists he enjoys a reputation similar to the likes of Albert Einstein -- who was a close friend. Born in 1906 in what was then Austria-Hungary and is now the Czech city of Brno, Gödel later studied in Vienna before moving to the United States after World War II broke out to work at Princeton, where Einstein was also based. The first version of this ontological proof is from notes dated around 1941, but it was not until the early 1970s, when Gödel feared that he might die, that it first became public.

Now Benzmüller hopes that using such a headline-friendly example can help draw attention to the method. "I didn't know it would create such a huge public interest but (Gödel's ontological proof) was definitely a better example than something inaccessible in mathematics or artificial intelligence," the scientist added. "It's a very small, crisp thing, because we are just dealing with six axioms in a little theorem. … There might be other things that use similar logic. Can we develop computer systems to check each single step and make sure they are now right?"

'An Ambitious Expressive Logic'

The scientists, who have been working together since the beginning of the year, believe their work could have many practical applications in areas such as artificial intelligence and the verification of software and hardware.

Benzmüller also pointed out that there are many scientists working on similar subject areas. He himself was inspired to tackle the topic by a book entitled "Types, Tableaus and Gödel's God," by Melvin Fitting.
The use of computers to reduce the burden on mathematicians is not new, even if it is not welcomed by all in the field. American mathematician Doron Zeilberger has been listing the name Shalosh B. Ekhad on his scientific papers since the 1980s. According to the New York-based Simons Foundation, the name is actually a pseudonym for the computers he uses to help prove theorems in seconds that previously required page after page of mathematical reasoning. Zeilberger says he gave the computer a human-sounding name "to make a statement that computers should get credit where credit is due." "human-centric bigotry" on the part of mathematicians, he says, has limited progress.

Ultimately, the formalization of Gödel's ontological proof is unlikely to win over many atheists, nor is it likely to comfort true believers, who might argue the idea of a higher power is one that defies logic by definition. For mathematicians looking for ways to break new ground, however, the news could represent an answer to their prayers.

http://arxiv.org/abs/1308.4526

By no means is this the right answer, but this is only an explanation that there are empirical scientific models that exist and respected scientists are testing this theory. In fact, there is an "on-going" study group on this theory.

 

[magnifier661]

http://www.ericsteinhart.com/articles/divineinfinity.pdf

On this pdf, there is another mathematical model theory of a divine infinite God.

ABSTRACT: Mathematics is obviously important in the sciences. And so it is likely to be equally important in any effort that aims to understand God in a scientifically significant way or that aims to clarify the relations between science and theology. The degree to which God has any perfection is absolutely infinite. We use contemporary mathematics to precisely define that absolute infinity. For any perfection, we use transfinite recursion to define an endlessly ascending series of degrees of that perfection. That series rises to an absolutely infinite degree of that perfection. God has that absolutely infinite degree. We focus on the perfections of knowledge, power, and benevolence. Our model of divine infinity thus builds a bridge between mathematics and theology.

 

[SlyPokerDog]

So to believe in god no longer requires faith but a degree in mathematics?

 

[magnifier661]

Now on the objections with the atheist, using respected scientist throughout history. Now it doesn't mean they believe in God, but it definitely suggests that they agree that the concept of God is a "REAL POSSIBILITY"

 

[magnifier661]

Here is an interesting link on math equations on the divine equation

http://www.mathmonism.com/eulersidentity.html

 

[magnifier661]

So to believe in god no longer requires faith but a degree in mathematics?

That's weird. The arguments say there are no scientific evidence on the concept of God. Then once I post a mathematical equation (scientific) and you make a joke that you don't require faith?

 

[magnifier661]

https://www.physicsforums.com/threads/mathematical-argument-for-the-existence-of-god.9553/

1.] If it is possible for a mind to perfectly understand[model] every aspect and detail of reality, then the mind that perfectly models reality is a super-intelligence, for all intents and purposes, the super-intelligence is God.[ This is self evident. No human[sub-sentient] mind will ever be able to know every aspect and detail of the universe from its beginning to its ending. We are the products of a creator, we are not "the" Creator.]

2.]If the perfect correspondence can be approached via a convergent analytic-synthetic propositional "limit", then the limit exists, even though a sentient mind within reality can only approach the limit.
[ All that needs to be proven is that the limit converges. No "sub-sentient" mind within creation itself can know every aspect of ...creation itself.]


3.] If the limit exists, the exact mental correspondence exists in the mind of a super-intelligence.
[self evident]



4.] That is to say, if the limit exists then a description exists.
[another way of stating 3.]


5.] If the description exists then the "describer" exists, since the description is "isomorphic"[ one to one and onto].

6.]The describer is a super-intelligence.

7.] By definition, the super-intelligence is God.

The burden of proof becomes the burden of proving the "convergence", to an exact correspondence, between the mental construct[infinite number of axioms] and reality

At the limit

[MIND]<--->[REALITY]

M = R

[axiomatic method]--->[exact correspondence]<---[scientific method]

 

[SlyPokerDog]

That's weird. The arguments say there are no scientific evidence on the concept of God. Then once I post a mathematical equation (scientific) and you make a joke that you don't require faith?

More of a smart ass remark than a joke.

Just having some fun.

Sorry, didn't mean any disrespect.

 

[magnifier661]

More of a smart ass remark than a joke.

Just having some fun.

Sorry, didn't mean any disrespect.

Sorry if I snapped at you. This is mainly a response to Denny and his remarks "Science and God are not compatible". Also, his claims that there are no "empirical evidence" on the existence or concept of God.

So I do agree that there must be a level of "Faith" required to believe in God, it doesn't take away that there is still empirical evidence that God does exist.

 

[e_blazer]

From the title to this thread, I thought you had gone all Barfo in your approach to this:

Supermodels exist, therefore there is a god.

 

[magnifier661]

From the title to this thread, I thought you had gone all Barfo in your approach to this:

Supermodels exist, therefore there is a god.

LMAO!!!!!

 

[magnifier661]

[video=youtube;LFSRTsLOiv0]

Watch this video. It even talks about how science cannot measure "consciousness".

 

[andalusian]

Godel's work is fascinating, but claiming that is proves god's existence is a contradiction with the theory itself - because by accepting Godel's work as an axiom and using it to prove the existence of God within it's system you break Godel's theory that you can prove all the things in the system without getting out of it.

All Godel's work really says is that you can not prove everything within the system, you will always need something out of the system to do so. If this thing is god, a giant turtle floating through space with 4 elephants on it holding the discworld or a manifestation of PapaG's rants - we can not tell...

You can take the same theorem and apply it to, say, the bible - as your set of axioms - and given that it is your system - using Godel you show that mathematically it is impossible to prove the bible's axiom so any argument that says "because it is in the bible" is bunk.

FWIW - I love "Godel, Escher, Bach" - a really interesting book about cognitive functions. http://en.wikipedia.org/wiki/Gödel,_Escher,_Bach

 

[magnifier661]

Godel's work is fascinating, but claiming that is proves god's existence is a contradiction with the theory itself - because by accepting Godel's work as an axiom and using it to prove the existence of God within it's system you break Godel's theory that you can prove all the things in the system without getting out of it.

All Godel's work really says is that you can not prove everything within the system, you will always need something out of the system to do so. If this thing is god, a giant turtle floating through space with 4 elephants on it holding the discworld or a manifestation of PapaG's rants - we can not tell...

You can take the same theorem and apply it to, say, the bible - as your set of axioms - and given that it is your system - using Godel you show that mathematically it is impossible to prove the bible's axiom so any argument that says "because it is in the bible" is bunk.

FWIW - I love "Godel, Escher, Bach" - a really interesting book about cognitive functions. http://en.wikipedia.org/wiki/Gödel,_Escher,_Bach

I will agree that this can be applied for any situation, but that's what makes the model so important. It is the main reason why most atheist hold onto a agnostic approach on the existence of God. There is "always" a possibility for this to be truth, because this model makes it so. Doesn't mean it is so, but it definitely proves that there is no irrefutable proof there isn't.

Look at the other models. They are pretty cool too. Or the concept that the Universe has "uniformity", using the Golden Rule. Again, this isn't a "irrefutable" proof God exists, but the probability the universe has purpose or design is highly probable.

 

[andalusian]

Look at the other models. They are pretty cool too. Or the concept that the Universe has "uniformity", using the Golden Rule. Again, this isn't a "irrefutable" proof God exists, but the probability the universe has purpose or design is highly probable.

Remove the "highly" and I agree.

I agree that there is a probability that something like a God exists, I will say however that the probability that it is anything like what humans tell us through anyone of the millions of religions is infinitesimally small, so my advice, if you want to be a gambling man and believe in one - is to make up in your mind what is needed of you without any need to reference existing religions, because you are just as likely to hit it right and be in it's good graces with your own made up rules as you are with religion X's rules.

 

[magnifier661]

Remove the "highly" and I agree.

I agree that there is a probability that something like a God exists, I will say however that the probability that it is anything like what humans tell us through anyone of the millions of religions is infinitesimally small, so my advice, if you want to be a gambling man and believe in one - is to make up in your mind what is needed of you without any need to reference existing religions, because you are just as likely to hit it right and be in it's good graces with your own made up rules as you are with religion X's rules.

I agree with most of what you say. I question everything, even my faith. I think a logical man would do such a thing.

I've also played with the concept of a conscious universe. It seems logical and could explain how the universe could have an "absolute beginning" and being eternal, which is completely compatible. I choose the Jehovah God, just because it fits best for me. But as I have already proven many times before, I am not of the same mold of most Christians.

 

[tlongII]

Remove the "highly" and I agree.

I agree that there is a probability that something like a God exists, I will say however that the probability that it is anything like what humans tell us through anyone of the millions of religions is infinitesimally small, so my advice, if you want to be a gambling man and believe in one - is to make up in your mind what is needed of you without any need to reference existing religions, because you are just as likely to hit it right and be in it's good graces with your own made up rules as you are with religion X's rules.

I would replace probability with possibility. There is nothing I am aware of that would argue that something "God-like" is probable. It's certainly possible though.

 

[MarAzul]

Sorry if I snapped at you. This is mainly a response to Denny and his remarks "Science and God are not compatible". Also, his claims that there are no "empirical evidence" on the existence or concept of God.

So I do agree that there must be a level of "Faith" required to believe in God, it doesn't take away that there is still empirical evidence that God does exist.

Actually sense you are delving into the possible mathematical probabilities of god. I will disagree with where the faith is needed. I think when to take this concept far enough you will find the faith is require to believe god does not exist.

 

[andalusian]

I would replace probability with possibility. There is nothing I am aware of that would argue that something "God-like" is probable. It's certainly possible though.

I meant Probability in the mathematical sense - where you assign percentages to the likelihood that a statement/event is true.

 

[Further]

It's an interesting approach to take to the question of the existence of God, but my level of mathematics is fairly low so understanding all the math is not possible for me.

For me, there are a few parts to the question.
1) I can't disprove God, so it remains a possibility no matter how remote.
2) From the beginning of time till now everything needs to fit together like a puzzle, some questions answered and some unanswered, but enough logic for me to hold that there is no requirement of any outside guidance (God) to play any role since time began.
3) there is no way for us to understand what preceded the Big Bang but none of our laws would hold true then, so if there were any type of force I can't understand (including God) this is the most likely place for it to present itself.

But since I live in the world after time began and have no idea how to comprehend the preceding everything, I must base my belief structure on the period that is potentially knowable. God is possible, but totally unlikley.

 

[MarAzul]

It's an interesting approach to take to the question of the existence of God, but my level of mathematics is fairly low so understanding all the math is not possible for me.

Have you every rationalized why you differ with a man like Kurt Gödel? Since you admit to different skill level in math with him, how do you justify arriving at the opposite result in this question?

 

[magnifier661]

It's an interesting approach to take to the question of the existence of God, but my level of mathematics is fairly low so understanding all the math is not possible for me.

For me, there are a few parts to the question.
1) I can't disprove God, so it remains a possibility no matter how remote.
2) From the beginning of time till now everything needs to fit together like a puzzle, some questions answered and some unanswered, but enough logic for me to hold that there is no requirement of any outside guidance (God) to play any roll since time began.
3) there is no way for us to understand what preceded the Big Bang but none of our laws would hold true then, so if there were any type of force I can't understand (including God) this is the most likely place for it to present itself.

But since I live in the world after time began and have no idea how to comprehend the preceding everything, I must base my belief structure on the period that is potentially knowable. God is possible, but totally unlikley.

Could that be considered a certain "ignorance"? I'm not calling you out in a negative way. Just because we may be ignorant to the spiritual level, could mean that we just can't see it. Possibly through conscious evolution, you start understanding the realm more easily?

 

[Further]

Could that be considered a certain "ignorance"? I'm not calling you out in a negative way. Just because we may be ignorant to the spiritual level, could mean that we just can't see it. Possibly through conscious evolution, you start understanding the realm more easily?

It could certainly be ignorance. I am confined by what I know and am therefor ignorant of quite a bit. But I can't base my conclusions on what I don't know. That why, although I am an athiest, I am always open to changing my mind if I learn something that negates my previous belief.

 

[magnifier661]

It could certainly be ignorance. I am confined by what I know and am therefor ignorant of quite a bit. But I can't base my conclusions on what I don't know. That why, although I am an athiest, I am always open to changing my mind if I learn something that negates my previous belief.

Sounds fair. I can respect that.

 

[Further]

Have you every rationalized why you differ with a man like Kurt Gödel? Since you admit to different skill level in math with him, how do you justify arriving at the opposite result in this question?

There are plenty of Nobel laureates (all brighter than me) who believe in God and who don't believe in God. I will generally put more weight to the words of brilliant people, but I don't simply accept their conclusions without contemplation either, especially if many brilliant people disagree.

 

[MarAzul]

There are plenty of Nobel laureates (all brighter than me) who believe in God and who don't believe in God. I will generally put more weight to the words of brilliant people, but I don't simply accept their conclusions either, especially if many brilliant people disagree.

I only know of two people that have applied mathematics to the question of Gods existence, Mags and Kurt Gödel. Do you think neither have the weight to bring you to reconsidering your conclusions?

 

[Further]

Not from what I have seen. Kurt Gödel may have been one of few to originally apply math to the question, but many other brilliant people have dissected that work and found problems with some assertions and conclusions. The issue is far from settled so no, the conclusions of of Gödel are insufficient for me. As far as mags goes, his best argument is one he has yet to use, his wife.

 

[magnifier661]

Not from what I have seen. Kurt Gödel may have been one of few to originally apply math to the question, but many other brilliant people have dissected that work and found problems with some assertions and conclusions. The issue is far from settled so no, the conclusions of of Gödel are insufficient for me. As far as mags goes, his best argument is one he has yet to use, his wife.

hahahahaha

 

[magnifier661]

Keep in mind there are 4 mathematical models for God. I know Godell's is more famous, but the concept is "you can build a model for the existence of God"; which was argued could not be the case

 

[MarAzul]

Not from what I have seen. Kurt Gödel may have been one of few to originally apply math to the question, but many other brilliant people have dissected that work and found problems with some assertions and conclusions. The issue is far from settled so no, the conclusions of of Gödel are insufficient for me. As far as mags goes, his best argument is one he has yet to use, his wife.

I would be interested to hear who these people are that disagreed with Gödel. We are speaking of mathematics, assertions disagreed with would be very interesting, deducing assertions from math work is very unusual.