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Proof of the existence of God set down on paper

Sounds like a restatement of the ontological argument. Can be disproved by comparison; Envisaging a 'perfect island' does not necessitate the existence of a perfect island.
 
Temporal Renegade said:
According to the io9.com website, a fellow named Kurt Gödel came up with what he believed to be the proof of the existence of God on paper.

His argument went something like this: God is the greatest being in the Universe. If God *didn't* exist, another would HAVE to exist; and, since it wasn't possible to imagine one more powerful, then God exists.


Glad THAT is all cleared up......
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That is not a good representation of Gödel's proof. It is more like "Being Godlike is a property that cannot entail it's own negation and is therefore possible and if a being with necessary existence is possible then it exists". Although that is a quick and dirty simplification.

The Wiki article on it is quite good : http://en.wikipedia.org/wiki/Gödel's_ontological_proof
 
There are some pretty waffly terms in there.

I can imagine the greatest baseball player. I can also imagine the greatest basketball player. Do those have to be the same thing/person?

I don't see why imagining the "greatest being" would necessarily be mathematically possible or get past the, "greatest current being" or some such.

I suppose, to do the argument justice, we'd have to track down another entity -- "the greatest living imaginer." To do that, I suggest finding, "the greatest tracker downer."

I would like to propose that the lack of a God is a more perfect state of affairs and base my ontological argument on my idea of necessary perfection. But to give it real heft, I'm going to have to become a famous scientist or mathematician first. Please be patient.
 
Temporal Renegade said:
According to the io9.com website, a fellow named Kurt Gödel came up with what he believed to be the proof of the existence of God on paper.

His argument went something like this: God is the greatest being in the Universe. If God *didn't* exist, another would HAVE to exist; and, since it wasn't possible to imagine one more powerful, then God exists.


Glad THAT is all cleared up......
Click to expand...


From the website:

God can either necessarily exist, or necessarily not exist. If God is an all-powerful being, and he exists, he necessarily exists in all possible worlds. If he doesn't exist, he necessarily doesn't exist in any possible worlds. It is not possible to say that God does not exist in any possible world. No matter how slim the chance is, God might exist. That means that God can't necessarily not exist. Since the choices are either God necessarily does exist, or necessarily doesn't, and we have eliminated the possibility that he necessarily doesn't, the only possibility left is that he necessarily does.


Looks like a really tiny gap.

The word "necessarily' seems to have been added to make it look more impressive.
 
tsig said:
The word "necessarily' seems to have been added to make it look more impressive.
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The word "necessary" has a certain meaning in logic.
The statement P => Q can be as:
- If P is true then Q is true
- If Q is false then P is false
- P is true only if Q is true
- P true is sufficient for Q to be true
- Q is true is necessary for P to be true.

So if P is true then Q is necessarily true. The OP seems to be saying that IF God exists at all THEN he must necessarily exist in ALL worlds. The contrapositive would be IF there is a world where God doesn't exist THEN God doesn't exist at all.

A nice exercise in logic but it doesn't answer any questions. Even the bit about God necessarily existing in all worlds if He exists at all is an unproven assertion.
 
I read about this in io9.com, too. But it explains that this was merely an exercise in math logic, rather than actually trying to prove the existence of god:

There's no doubt that Gödel was a brilliant man - he was a good friend of Albert Einstein's, who admired him greatly. It is also thought that, during his life, he had certain religious and mystical convictions. However, he specifically held the proof back during his lifetime because he didn't wish it to be taken as 'his proof that God exists'. He, in fact, didn't want people to think he believed in God at all. He was clear that the entire proof was simply an exercise in modal logic, derived from a certain set of assumptions. Those assumptions can be questioned. For example, Gödel's definition of God didn't have anything to do with the behavior of a deity, it was just a variation on St. Anselm's 'greatest imaginable being'. In other words, it was an axiom specifically chosen for both a vague sense of religion and the ability to make the rest of the proof work. If someone defined God differently - the being that made the world in seven days, for example - then the proof no longer applies. There have plenty of atheist thinkers knocking down the proof. And plenty of theist thinkers expanding on it.
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http://io9.com/5805775/proof-of-the-existence-of-god-set-down-on-paper
 
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OK, how about this for a refutation:

A supreme being can be imagined as the greatest possible entity
A supreme being would have created the universe, created the heavens and the earth, and created all life
A being that could create the universe while not itself existing is greater than a being that has to exist in order to create the universe.
Therefore God does not exist.
 
psionl0 said:
The word "necessary" has a certain meaning in logic.
The statement P => Q can be as:
- If P is true then Q is true
- If Q is false then P is false
- P is true only if Q is true
- P true is sufficient for Q to be true
- Q is true is necessary for P to be true.

So if P is true then Q is necessarily true. The OP seems to be saying that IF God exists at all THEN he must necessarily exist in ALL worlds. The contrapositive would be IF there is a world where God doesn't exist THEN God doesn't exist at all.

A nice exercise in logic but it doesn't answer any questions. Even the bit about God necessarily existing in all worlds if He exists at all is an unproven assertion.
Click to expand...

Granted that it has a meaning in logic but you can read the whole passage with the word "necessarily" removed and the meaning is the same.
 
Lamuella said:
OK, how about this for a refutation:

A supreme being can be imagined as the greatest possible entity
A supreme being would have created the universe, created the heavens and the earth, and created all life
A being that could create the universe while not itself existing is greater than a being that has to exist in order to create the universe.
Therefore God does not exist.
Click to expand...


My god = (your god) + 1
 
Robin said:
That is not a good representation of Gödel's proof. It is more like "Being Godlike is a property that cannot entail it's own negation and is therefore possible and if a being with necessary existence is possible then it exists". Although that is a quick and dirty simplification.

The Wiki article on it is quite good : http://en.wikipedia.org/wiki/Gödel's_ontological_proof
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Everybody seems to be debating Gödel's proof as though it was Anselm's proof.
 
God Santa Clause can either necessarily exist, or necessarily not exist. If God Santa Clause is an all-powerful being, and he exists, he necessarily exists in all possible worlds. If he doesn't exist, he necessarily doesn't exist in any possible worlds. It is not possible to say that God Santa Clause does not exist in any possible world. No matter how slim the chance is, God Santa Clause might exist. That means that God Santa Clause can't necessarily not exist. Since the choices are either God Santa Clause necessarily does exist, or necessarily doesn't, and we have eliminated the possibility that he necessarily doesn't, the only possibility left is that he necessarily does.
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I fixed their quote.
 
tsig said:
God can either necessarily exist, or necessarily not exist.
Click to expand...

The problem with logical proofs is that they usually demonstrate a confining lack of imagination. This opening statement, for example, overlooks the possibility of a being with conditional existence. Is it not conceivable that a being might exist only if others believe it exists?
 
Ray Brady said:
The problem with logical proofs is that they usually demonstrate a confining lack of imagination. This opening statement, for example, overlooks the possibility of a being with conditional existence. Is it not conceivable that a being might exist only if others believe it exists?
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If he were subject to the whims of believers, then he would be, by definition not "all powerful" and not the god discussed in the proof.

I think Godel's proof as I understand it rings valid.
I must admit, I can't read the formal, symbol based version, but from the paraphrasing:

A: Define God as a being that is all powerful.

B(unstated): Define "all powerful" as the ability to do anything, in all possible universes.

C: The probability of such a god existing is non-zero.

D: For any event with a non-zero probability, there is, by definition, a possible universe in which it exists.

E: If a god exists in only one, but not all possible universes, then he is by definition, not "all powerful" and so exists in zero universes.

F: Since we've already concluded that this god exists in at least one possible universe (from C +D), then the conditions for E are not met and this god must exist in all possible universes, including our own.


It's actually a much more clever formulation of the ontological argument, and it's a bit more internally consistent than most. My problem is with the premises B+C. The definition of a being which is all powerful is logically self-contradictory (A rock so big he can't lift it etc) which means there is an actual zero probability that he exists in a possible universe.

However, if there wasn't this problem with the premise, the rest of the logic would work.
 
Cavemonster said:
It's actually a much more clever formulation of the ontological argument, and it's a bit more internally consistent than most. My problem is with the premises B+C. The definition of a being which is all powerful is logically self-contradictory (A rock so big he can't lift it etc) which means there is an actual zero probability that he exists in a possible universe.

However, if there wasn't this problem with the premise, the rest of the logic would work.
Click to expand...

That's a really good refutation Cavemonster. I'll have to remember it.
 
Cavemonster said:
If he were subject to the whims of believers, then he would be, by definition not "all powerful" and not the god discussed in the proof.

I think Godel's proof as I understand it rings valid.
I must admit, I can't read the formal, symbol based version, but from the paraphrasing:

A: Define God X* as a being that is all powerful.

B(unstated): Define "all powerful" as the ability to do anything, in all possible universes.

C: The probability of such a god existing is non-zero.

D: For any event with a non-zero probability, there is, by definition, a possible universe in which it exists.

E: If a god exists in only one, but not all possible universes, then he is by definition, not "all powerful" and so exists in zero universes.

F: Since we've already concluded that this god exists in at least one possible universe (from C +D), then the conditions for E are not met and this god must exist in all possible universes, including our own.


It's actually a much more clever formulation of the ontological argument, and it's a bit more internally consistent than most. My problem is with the premises B+C. The definition of a being which is all powerful is logically self-contradictory (A rock so big he can't lift it etc) which means there is an actual zero probability that he exists in a possible universe.

However, if there wasn't this problem with the premise, the rest of the logic would work.
Click to expand...

*X = Allah, Yahweh, The Divine Principle, The Great Green Arklesiezure, ect, ect, ect.
 
tsig said:
*X = Allah, Yahweh, The Divine Principle, The Great Green Arklesiezure, ect, ect, ect.
Click to expand...

Yes, Godel's proof has nothing to do with any particular religious tradition, or any particular name really.

However, it is necessary for there to be only one.

Even if you're not convinced that the very idea of "all powerful" is self contradictory, then it must be clear that the idea of multiple "all powerfuls" is a logical contradiction. By definition, they could not act against the goals of each other. If Beings X and Y are both all powerful then they would each have the ability to foil the other's plans, which creates an immediate contradiction.
 
Cavemonster said:
If he were subject to the whims of believers, then he would be, by definition not "all powerful" and not the god discussed in the proof.

I think Godel's proof as I understand it rings valid.
I must admit, I can't read the formal, symbol based version, but from the paraphrasing:

A: Define God as a being that is all powerful.

B(unstated): Define "all powerful" as the ability to do anything, in all possible universes.

C: The probability of such a god existing is non-zero.

D: For any event with a non-zero probability, there is, by definition, a possible universe in which it exists.

E: If a god exists in only one, but not all possible universes, then he is by definition, not "all powerful" and so exists in zero universes.

F: Since we've already concluded that this god exists in at least one possible universe (from C +D), then the conditions for E are not met and this god must exist in all possible universes, including our own.


It's actually a much more clever formulation of the ontological argument, and it's a bit more internally consistent than most. My problem is with the premises B+C. The definition of a being which is all powerful is logically self-contradictory (A rock so big he can't lift it etc) which means there is an actual zero probability that he exists in a possible universe.

However, if there wasn't this problem with the premise, the rest of the logic would work.
Click to expand...

No. Not only wouldn't it, it doesn't.

Half the argument treats universes as independent, the other half treats them as interconnected. God is at one point given a chance to exist of x per Universe, but is then defined in a way that doesn't allow for independent existence or non-existence across universes. If's in all-or-nothing question, we only have to look at the entire multi-verse.

Of course, all that would assume that I am accepting the ridiculous premises that God's existence in any given Universe would be a chance parameter, like life-supporting planets or super novae. There is no reason to assume that the chances of God existing are x for a given Universe like hours. To say that, we would need a count; and we would need to know about other Universes. God is or isn't - chance most certainly doesn't play a role in it. The question is meanignless. How big are the "chances" that I exist? There is no "chance". I just do - period.

ETA: And how does one come to the conclusion that the chances are > 0 in the first place? What makes a god possible?
 
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Cavemonster said:
It's actually a much more clever formulation of the ontological argument, and it's a bit more internally consistent than most. My problem is with the premises B+C. The definition of a being which is all powerful is logically self-contradictory (A rock so big he can't lift it etc) which means there is an actual zero probability that he exists in a possible universe.

However, if there wasn't this problem with the premise, the rest of the logic would work.
Click to expand...

I like the formlation as probability. Either something does or does not exist, i.e. either the probability is 0 or 1. How was that premise again?
C: The probability of such a god existing is non-zero.​
Though luck with getting that one through.



What I don't like is "A rock so heavy..." - that is just daft. :p I guess the omnipotence here does have to dance to the tune of what is possible.
 
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Rasmus said:
The question is meanignless. How big are the "chances" that I exist? There is no "chance". I just do - period.
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Really? As far as I know, it's not impossible that "you" are a computer program, a bunch of pygmy mice dancing on a keyboard, or a figment of my imagination.

Are you saying it is absolutely 100% impossible for any of those things to be true, or just astronomically unlikely?

Our information about the world we observe will always be incomplete, everything we know to "exist" is just our model of what most likely exists given available information.

A study was done recently where students were shown a commercial for popcorn. One group tired the product afterwards, another did not. The one that did not actually try the popcorn was fairly likely to believe they had and give an opinion on the product, only a week later.

The whole basis of science is that we construct models to describe our current understanding of the world, and that there is a chance we're wrong about anything.


Rasmus said:
ETA: And how does one come to the conclusion that the chances are > 0 in the first place? What makes a god possible?
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Whatever is not impossible is possible. Without more information, we can't say how likely it is, but until we rule it out, it remains a possibility.
 
Lord Emsworth said:
I like the formlation as probability. Either something does or does not exist, i.e. either the probability is 0 or 1. How was that premise again?
C: The probability of such a god existing is non-zero.​
Though luck with getting that one through.



What I don't like is "A rock so heavy..." - that is just daft. :p I guess the omnipotence here does have to dance to the tune of what is possible.
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See my response to Rasmus.
If we had perfect knowledge of the universe, then we'd be able to say everything that exists and everything that doesn't. Until we have that knowledge, all we have are probabilities. Some so high we can basically take them for granted, some so low we can ignore them.
 
Cavemonster said:
Whatever is not impossible is possible. Without more information, we can't say how likely it is, but until we rule it out, it remains a possibility.
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No, in order to accept a premise we need to be (reasonably) certain of its truth. If that has not been established, its either "No" or "I don't know".
 
Cavemonster said:
Really? As far as I know, it's not impossible that "you" are a computer program, a bunch of pygmy mice dancing on a keyboard, or a figment of my imagination.
Click to expand...

So?

Are you saying it is absolutely 100% impossible for any of those things to be true, or just astronomically unlikely?
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I am saying it has not been established that an entity like a god is possible. Feel free to demonstrate otherwise, though.

Our information about the world we observe will always be incomplete, everything we know to "exist" is just our model of what most likely exists given available information.
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So?
A study was done recently where students were shown a commercial for popcorn. One group tired the product afterwards, another did not. The one that did not actually try the popcorn was fairly likely to believe they had and give an opinion on the product, only a week later.
Click to expand...

What does this have to do with anything?
The whole basis of science is that we construct models to describe our current understanding of the world, and that there is a chance we're wrong about anything.
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So?

Whatever is not impossible is possible.
Click to expand...

You don't say? Did you come up with that all by yourself or did you have help?


Without more information, we can't say how likely it is, but until we rule it out, it remains a possibility.
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And this is where you are utterly wrong. Something remains impossible even if we don't know that it is. Traveling faster than light was not possible before Einstein proved that it was impossible. Thewre wasn't a >0 chance that Einstein would have proven FTL travel to be achievable. He only ever had two options: To either prove it impossible or to make a mistake.

Imagine an argument predating Einstein that relied on FTL travel being possible. It would have been useless.
 
The problem with this is, it only proves is that the person formulating the “proof” is able to use rules of logic to make up an argument, not that what it hopes to prove, is real.
I guess another way of putting it is they only prove that they can dream up rationales for what they desire already.
 
Cavemonster said:
The whole basis of science is that we construct models to describe our current understanding of the world, and that there is a chance we're wrong about anything.
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I think the mistake here is in confusing models with reality.

When I flip a fair coin, I assign a probability of 0.5 that it came up heads and 0.5 that it came up tails. But that's just a model based on my own state of partial information about the coin. Those probabilities are not properties of the coin itself, the coin either came up heads or it came up tails.

Cavemonster said:
Whatever is not impossible is possible. Without more information, we can't say how likely it is, but until we rule it out, it remains a possibility.
Click to expand...

It remains a possibility just like how after I've flipped my coin it remains a possibility that it came up heads. However, once we actually look at the coin we must update our beliefs upwards for one result and downwards for the other.
 
Lord Emsworth said:
No, in order to accept a premise we need to be (reasonably) certain of its truth. If that has not been established, its either "No" or "I don't know".
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I've never before met a person who didn't accept the existence of the word "possible".

Good luck with that.
 
Well, that has got to be the dumbest "Proof" I've ever seen.

He may not be able to imagine a more powerful God, but I can, so there!!!
 
kedo1981 said:
The problem with this is, it only proves is that the person formulating the “proof” is able to use rules of logic to make up an argument, not that what it hopes to prove, is real.
I guess another way of putting it is they only prove that they can dream up rationales for what they desire already.
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Absolutely. Every time I see something like this I think to myself, "Last I checked, you can't logic something into existence." Until the arguer can show that all the premises about the nature of the deity in question are accurate, it seems like a bunch of mental gymnastics to me.
 
Cavemonster said:
I've never before met a person who didn't accept the existence of the word "possible".

Good luck with that.
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Why shouldn't I accept the existence of the word "possible"? (Have I said something incredibly stupid somewhere?)

That aside, watch out that you don't equivocate of different meanings of "possible."
 
Moon-Spinner said:
Well, that has got to be the dumbest "Proof" I've ever seen.

He may not be able to imagine a more powerful God, but I can, so there!!!
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As I said before - the OP does not represent Godel's argument at all. So why is everybody acting as though it did?

Godel's argument says nothing about not being able to imagine a more powerful God. Nothing.
 
tsig said:
From the website:

#1 God can either necessarily exist, or necessarily not exist. #2 If God is an all-powerful being, and he exists, he necessarily exists in all possible worlds. #3 If he doesn't exist, he necessarily doesn't exist in any possible worlds. #4 It is not possible to say that God does not exist in any possible world. #5 No matter how slim the chance is, God might exist. #6 That means that God can't necessarily not exist.#7 Since the choices are either God necessarily does exist, or necessarily doesn't, and we have eliminated the possibility that he necessarily doesn't, the only possibility left is that he necessarily does.


Looks like a really tiny gap.

The word "necessarily' seems to have been added to make it look more impressive.
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Let's accept #1, #2 and #3. Now let's change # 4, It is not possible to say that god does absolutely, without doubt, exist in any possible world. Where is the absolute proof of that? My phrase is as valid as the original. #5 then has to change too. No matter how slim the chance is, god might not exist. #6 would read, that means that god can't necessarily exist. We have eliminated the possibility that he necessarily exists, we are left only with the possibility #7, that god does not exist.


kedo1981 said:
The problem with this is, it only proves is that the person formulating the “proof” is able to use rules of logic to make up an argument, not that what it hopes to prove, is real.
I guess another way of putting it is they only prove that they can dream up rationales for what they desire already.
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I agree. I'm sure that Godel was indeed extremely intelligent. The only explanation that I can think of why intelligent persons go through such tortuous logic to rationalize a belief in god, is the obvious fallacy of thinking that belief in god is in itself a virtue. Most people like to consider themselves good persons, not evil atheists.
 
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