Prove that God doesn't exist.

[numinus]

Numinus, you have a logical error in your reasoning.

Let U be the universal set of all possible things that can be done.
Let O = set of elements of all things God can do.
Let f be an element of U = "God can create a stone that he cannot lift."
The element f represents a fallibility or failure.

Agnapostate's argument can be stated,

1. Either f is an element of O or f is not an element of O.

2. If f is an element of O then God has an element of fallibility.

3. If f is not an element of O, then O is a proper subset of U, and God can't do all things.

4. Therefore the set O either consists of a fallibility or it is not universal.

Numinus, where your logic fails is in what do you do with the element f?
In your step 3. You say O complement is empty.
Therefore f must not be in O complement, because O complement is empty.
Therefore, since O and O complement are disjoint, f must be in O.
Therefore O has an element of fallibility.

Your statement 3. is in error, because O complement is not empty.
Therefore your statement 4. O complement is a subset of O is a logical contradiction.

Nonsense.

The premise is that god can do everything. You were proving that such a premise leads to a contradiction.

Therefore, O is a universal set and its complement is an empty set and f (if you wish to know its place in the scheme of logic) is a nullary element.

If O is not a universal set, then you merely assumed the statement you are seeking to prove, that god indeed, is fallible.

Oh, and btw, if you wish to refute a formal logical argument, you might want to give the proof for each statement. As your post stands, it is nothing more than a bunch of statments WITHOUT PROOF.

 

[numinus]

You know... in a free country there's nothing wrong with having unprovable beliefs or believing in Fable as fact.

This has happened all through history and it really just matters on how much the "story" is picked up on and who buys into it.

We all know about Santa Claus and how that real person, a good man that made and gave gifts to children of a small village... evolved over time to a magician living at the North Pole with hundreds of Elves making toys for delivery by magic sleigh & flying Reindeer all over the world all in one night.

Or there's the true historical facts of Vlad the Impaler would was a leader of forces in Transylvania. He would impale captured prisoners and display them on the stakes at the entrance to his country to scare off future his adversaries... that evolved through tale to a pale, blood sucking, Count Dracula vampire that could only be killed by he himself being stabbed in the heart with a stake.

So push whatever story you want or makes you personally feel better... but it's still just another evolved, way out of reality, tale.

I provided ONTOLOGICAL ARGUMENTS. They are arguments for the existence of GOD WITHOUT using biblical texts.

How many more times do I need to say this before you give yourself leave to understand, eh?

You wish to see a miracle of a truly grand scale? The universe is expanding. Lambda, the negative tensile tendency that keeps it expanding, is being CREATED out of NOTHING. That is the consequence of your precious LAMBDA-CDM cosmological model -- hidden beneath the heap of equations you cannot make heads or tails of.

And yes, in your country, you are free to believe that as well.

Pweh!

 

[9sublime]

Just because we do not fully understand the expansion of the universe, does not mean we have to attribute it to God.

In the past, when we didn't understand tsunamis, disease etc. we attributed them to God. Its exactly the same thing.

The only reason religion will always exist is because, if and when we solve everything we will still never know what happens when we die. As a result, people will fill the void of knowledge with religion rather than simply say "I don't know". But worst of all, I suspect they will carry on trying to force their bile of beliefs on other people.

 

[Dawkinsrocks]

Bang on the money.

They believe it because they want it to be true.

Not because there is eveidence.

They believe it in spite of the evidence.

And if another group behaved like this they would jump on them

 

[numinus]

Just because we do not fully understand the expansion of the universe, does not mean we have to attribute it to God.

In the past, when we didn't understand tsunamis, disease etc. we attributed them to God. Its exactly the same thing.

The only reason religion will always exist is because, if and when we solve everything we will still never know what happens when we die. As a result, people will fill the void of knowledge with religion rather than simply say "I don't know". But worst of all, I suspect they will carry on trying to force their bile of beliefs on other people.

Theology is as much a branch of human knowledge as the natural sciences. And while science is continously re-evaluating its models for a better understanding of the physical world, philosophers and theologians are continously re-evaluating the nature of their faith.

You are correct in saying that it is exactly the same thing -- more accurately, different fields of inquiry proceeding from different premises about two different aspects of the SAME THING.

As for the expanding universe, we are confronted by two different points of view -- spatial expansion attributed to the negative tensile energy of a curious nothingness, on the one hand, and a continuing process of creation initiated long ago on the other.

And I would suspect that the idea of a creative nothingness, especially within the scientific community, would have been preposterous had it not become intellectually fashionable to speculate the nature of nothingness and all that absurd pseudo-religious nihilist crap concocted by certifiably insane people (like nietzche) to begin with.

Now, I ask, who exactly is spreading bile around like candy -- the people who believe that there is some rational purpose in creation, a purpose that is good, or the people who, having found no particularly good reason for their miserable existence (and stupidly believe that there isn't any in others as well), believe everything is hurtling headlong to a complete and irreversible state of oblivion?

Let me guess -- you need to unleash that primal will to power residing in everyone's dank and dark psyche, destroy all vestiges of rational and logical restraint, and follow it like an instinct-driven beast to whatever sh1t-hole it leads us. Thus says zarathustra.

Pardon me if I don't follow suit.

 

[Dawkinsrocks]

That is a great exercise in wishful thinking and shows admirably how christians like to mix up a bit of science with their voodoo to sell it.

Classic

BTW Theology starts from a false premiss.

That is why it is irrelevant.

 

[Lagboltz]

The premise is that god can do everything.

That is neither of our premises. Your premise lies in the definition of O being constrained to "things God can do." It therefore is only a 'universe of discourse' not the type of universal set U which contains all possible objects.

You were proving that such a premise leads to a contradiction.

That was not my premise.
I first rephrased Agnapostate's argument using set theory, and introduced the element f.

I thought it was obvious what I was doing. I will explain it in more detail. First make definitions:
Let U = the universal set of discourse = all possible things that can be done.
Let O = set of elements of all things God can do. (Your definition.)
Let f be an element of U.

This is one level above your premise. Notice that I explicitly limit my universe of discourse U to action statements. To prove God can do everything, all we have to do is prove that the sets O and U are identical. If we show they are not identical, then we show that God cannot do all possible things.
It's as simple as that.
I formalized Agnapostate's statements in showing a contradiction to O = U by asking if element f (= 'God can create a stone that he cannot lift') was a member of O or O', where O' = U\O.

If O is not a universal set, then you merely assumed the statement you are seeking to prove, that god indeed, is fallible.

No, I made absolutely no assumption. I did not assume as a premise that O was a proper subset of U nor that O = U. The latter is what you tried to do without stating that O was a limited universe of discourse. You are the one who assumed the statement you wanted to prove.

Oh, and btw, if you wish to refute a formal logical argument, you might want to give the proof for each statement. As your post stands, it is nothing more than a bunch of statments WITHOUT PROOF.

I was not refuting your argument. I was formalizing Agnapostate's argument. You did not refute his argument.

I think you know the logical justification for each statement -- simple Logic 101. To save time, if you find any of the following four steps erroneous, state why and I will supply the proof.
1. Either f is an element of O or f is not an element of O.
2. If f is an element of O then God has an element of fallibility.
3. If f is not an element of O, then O is a proper subset of U, and God can't do all things.
4. Therefore the set O either consists of a fallibility or it is not universal.

To guide you in my thinking,
The two sets O and O' (O' = U\O) form a partition of U.
In Step 2 and 3, an element, f member of U, must be a member of one of the two partition sets.
Step 4 comments on the two choices but does not state which set f is a member of.

You did not answer my question: Is f an element of O as you defined it or not??

 

[top gun]

Just because we do not fully understand the expansion of the universe, does not mean we have to attribute it to God.

In the past, when we didn't understand tsunamis, disease etc. we attributed them to God. Its exactly the same thing.

The only reason religion will always exist is because, if and when we solve everything we will still never know what happens when we die. As a result, people will fill the void of knowledge with religion rather than simply say "I don't know". But worst of all, I suspect they will carry on trying to force their bile of beliefs on other people.

Spot on!

I myself see being Agnostic (open to the possibility of a God but also seeing no proof whatsoever) as being very open minded.

I think with questions about a God the possibilities of infinite power probably causes me to fall short of being Atheist. But still no proof is no proof... and I'm one to wait for some modern testable proof and not just passed down tales or shot in the dark philosophies..

 

[top gun]

I provided ONTOLOGICAL ARGUMENTS. They are arguments for the existence of GOD WITHOUT using biblical texts.

How many more times do I need to say this before you give yourself leave to understand, eh?

You wish to see a miracle of a truly grand scale? The universe is expanding. Lambda, the negative tensile tendency that keeps it expanding, is being CREATED out of NOTHING. That is the consequence of your precious LAMBDA-CDM cosmological model -- hidden beneath the heap of equations you cannot make heads or tails of.

And yes, in your country, you are free to believe that as well.

Pweh!

American Indians and the ancient Greeks did the exact same things explaining the world with their multiple "Gods".

The explanation for the whole universe could be just the wave of a magic wand a trillion years ago by a great sorcerer... or some ancient alien species that long since went back through some black hole to some alternate universe never able to return.

But that's not proof. That's blind faith on, for lack of better words... a wild guess.

 

[numinus]

That is neither of our premises. Your premise lies in the definition of O being constrained to "things God can do." It therefore is only a 'universe of discourse' not the type of universal set U which contains all possible objects.

That was not my premise.
I first rephrased Agnapostate's argument using set theory, and introduced the element f.

I thought it was obvious what I was doing. I will explain it in more detail. First make definitions:
Let U = the universal set of discourse = all possible things that can be done.
Let O = set of elements of all things God can do. (Your definition.)
Let f be an element of U.

This is one level above your premise. Notice that I explicitly limit my universe of discourse U to action statements. To prove God can do everything, all we have to do is prove that the sets O and U are identical. If we show they are not identical, then we show that God cannot do all possible things.
It's as simple as that.
I formalized Agnapostate's statements in showing a contradiction to O = U by asking if element f (= 'God can create a stone that he cannot lift') was a member of O or O', where O' = U\O.


No, I made absolutely no assumption. I did not assume as a premise that O was a proper subset of U nor that O = U. The latter is what you tried to do without stating that O was a limited universe of discourse. You are the one who assumed the statement you wanted to prove.


I was not refuting your argument. I was formalizing Agnapostate's argument. You did not refute his argument.

These are all dishonest nonsense.

The OMNIPOTENCE PARADOX was offered as a refutation against omnipotence. The paradox states that IF omnipotence is PREMISED (naively stated as the ability TO DO ANYTHING AND EVERYTHING), then such a premise would lead to an ANTIMONY (god being able to do and not do something AT THE SAME TIME).

The given set O, by virtue of the naive definition 'ANYTHING AND EVERYTHING', can only be interpreted as a UNIVERSAL SET -- hence the statement 'O is a universal set' and the proof being the naive definition of omnipotence.

Do you understand so far?

Now, if you are going to state as given:

U=universal set=all the thing that is possible to do
O=subset of U=things god can do

Then my statement 1 -- O is a universal set or O=U, stands for the very same reason -- the definition of omnipotence.

I think you know the logical justification for each statement -- simple Logic 101. To save time, if you find any of the following four steps erroneous, state why and I will supply the proof.
1. Either f is an element of O or f is not an element of O.
2. If f is an element of O then God has an element of fallibility.
3. If f is not an element of O, then O is a proper subset of U, and God can't do all things.
4. Therefore the set O either consists of a fallibility or it is not universal.

To guide you in my thinking,
The two sets O and O' (O' = U\O) form a partition of U.
In Step 2 and 3, an element, f member of U, must be a member of one of the two partition sets.
Step 4 comments on the two choices but does not state which set f is a member of.

You did not answer my question: Is f an element of O as you defined it or not??

I have already answered this -- f is a NULLARY ELEMENT. It is right there if you'd care to look at my post again. It is an element with vacuous truth -- an element where both NO CONDITIONS and ALL CONDITIONS APPLY.

In the real number system, there is a very strong analogy with the empty set and 0. That is why the set of integers I={i/i is positive, negative and 0} precisely because 0 is neither positive nor negative. And the analogy does not stop there. Division by 0, as in set theory, is RESTRICTED.

That is why set theory is said to be AXIOMATIZED.

Understand?

So you see, there is no error in my formal logic. The error lies in the naive definition of omnipotence, which was thoroughly discussed by Aquainas. And as I said, I preferred to think of it in the simplest manner possible (complex reasoning being a sign of defective truth) -- THAT GOD CAN CREATE A ROCK HE CANNOT LIFT AND PROCEEDS TO LIFT IT ANYWAY.

 

[numinus]

Spot on!

I myself see being Agnostic (open to the possibility of a God but also seeing no proof whatsoever) as being very open minded.

I think with questions about a God the possibilities of infinite power probably causes me to fall short of being Atheist. But still no proof is no proof... and I'm one to wait for some modern testable proof and not just passed down tales or shot in the dark philosophies..

That is NOT agnosticism. If it were, then it is the most bullsh1t form of agnosticism imaginable.

What is a more accurate statement is that YOU DO NOT KNOW, instead of pretending your ignorance to have some form of intellectual substance to begin with.

And what is supremely humorous is that you appear to have a lot to say about something that, by your own admission, you don't know.

Pweh!

 

[9sublime]

So you see, there is no error in my formal logic. The error lies in the naive definition of omnipotence, which was thoroughly discussed by Aquainas. And as I said, I preferred to think of it in the simplest manner possible (complex reasoning being a sign of defective truth) -- THAT GOD CAN CREATE A ROCK HE CANNOT LIFT AND PROCEEDS TO LIFT IT ANYWAY.

The logic is absoloutley impeccable. A total and utter contradiciton is fine if God is thrown into the equasion.

 

[Lagboltz]

These are all dishonest nonsense.

The OMNIPOTENCE PARADOX was offered as a refutation against omnipotence. The paradox states that IF omnipotence is PREMISED (naively stated as the ability TO DO ANYTHING AND EVERYTHING), then such a premise would lead to an ANTIMONY (god being able to do and not do something AT THE SAME TIME).

I absolutely agree that it is dishonest nonsense. I thought you were making an argument that omnipotence is so powerful that it allows both an action and the negation of the action to be allowed in the same set using a logical sophistry that plumbed the depths of idiocy. The reason I thought this was because of your conclusion in

Post #763, "The set of things god cannot do is an element of the set of things god can do -- hence god is omnipotent."

But since I see that you are now claiming the same thing that I'm claiming -- that it's all nonsense -- I guess we have no disagreement.

I have already answered this -- f is a NULLARY ELEMENT. It is right there if you'd care to look at my post again. It is an element with vacuous truth -- an element where both NO CONDITIONS and ALL CONDITIONS APPLY.

Being nullary has nothing to do with it's potential set membership for the particular sets we were talking about. You will have to supply proof of that. On the other hand, don't bother. I don't think you know as much about math as I first thought.

In the real number system, there is a very strong analogy with the empty set and 0. That is why the set of integers I={i/i is positive, negative and 0} precisely because 0 is neither positive nor negative.

You are now talking about group theory, not set theory, but you have a rather inane way of looking at it. The identity element 0 in the additive group has nothing to do with "emptyness". This is a meaningless digression.

And the analogy does not stop there. Division by 0, as in set theory, is RESTRICTED.

Now you are talking about field theory. I don't see any context here either.

That is why set theory is said to be AXIOMATIZED.
Understand?

You still seem to be rambling.

So you see, there is no error in my formal logic. The error lies in the naive definition of omnipotence, which was thoroughly discussed by Aquainas. And as I said, I preferred to think of it in the simplest manner possible (complex reasoning being a sign of defective truth) -- THAT GOD CAN CREATE A ROCK HE CANNOT LIFT AND PROCEEDS TO LIFT IT ANYWAY.

I would completely agree with you if your goal was Reductio ad Absurdum, but now you seem to be serious about your conclusion in post #763 again. But I will assume that I misread you and we can leave it at that.

 

[numinus]

The logic is absoloutley impeccable.

Of course predicate logic is impeccable. Hard to think of it otherwise. After all, human beings have been at it for five thousand years, maybe longer.

A total and utter contradiciton is fine if God is thrown into the equasion.

Nonsense. Set theory, its axioms and logical operations, were formalized by agnostics, fyi. The conclusions being presented are inescapable.

 

[numinus]

I absolutely agree that it is dishonest nonsense. I thought you were making an argument that omnipotence is so powerful that it allows both an action and the negation of the action to be allowed in the same set using a logical sophistry that plumbed the depths of idiocy. The reason I thought this was because of your conclusion in
But since I see that you are now claiming the same thing that I'm claiming -- that it's all nonsense -- I guess we have no disagreement.

Of course it is possible, if you are dealing with empty sets. I thought you've had figured that out by now.

Being nullary has nothing to do with it's potential set membership for the particular sets we were talking about. You will have to supply proof of that. On the other hand, don't bother. I don't think you know as much about math as I first thought.

Of course it does. Being a nullary element, which is what empty set is, relative to other sets, IS a member of ANY SET, not just a POTENTIAL MEMBER. The proof is from the DEFINITION OF SUBSET, which I believe I have already mentioned.

NO CONDITION applies on an empty set since, it has NO MEMBERS.

ALL CONDITIONS apply on an empty set since it is a SUBSET of ANY SET.

To make set theory ENTIRELY RATIONAL, it is necessary to state this AXIOM.

Understand?

You are now talking about group theory, not set theory, but you have a rather inane way of looking at it. The identity element 0 in the additive group has nothing to do with "emptyness". This is a meaningless digression.

Whoa. Not so fast cowboy.

First there is first order predicate logic (fopl) which gives rise to set theory which gives rise to a host of foundational theories in mathematics including number, group and field theories.

The example I gave demonstrates the nature of integers, which is rightly within number theory which itself is the next logical step to set theory.

The analogy is quite valid, as I would show in a while.

Who exactly is diressing, hmmm?

Now you are talking about field theory. I don't see any context here either.

You still seem to be rambling.

The binary operations of set union and intersection satisfy many identities. Several of these identities or "laws" have well established names. Three pairs of laws, are stated, without proof, in the following proposition.

PROPOSITION 1: For any sets A, B, and C, the following identities hold:
commutative laws:

associative laws:

distributive laws:

Notice that the analogy between unions and intersections of sets, and addition and multiplication of numbers, is quite striking. Like addition and multiplication, the operations of union and intersection are commutative and associative, and intersection distributes over unions. However, unlike addition and multiplication, union also distributes over intersection.

The next proposition, states two additional pairs of laws involving three specials sets: the empty set, the universal set and the complement of a set.

PROPOSITION 2: For any subset A of universal set U, where Ø is the empty set, the following identities hold:

identity laws:

complement laws:

The identity laws (together with the commutative laws) say that, just like 0 and 1 for addition and multiplication, Ø and U are the identity elements for union and intersection, respectively.

Unlike addition and multiplication, union and intersection do not have inverse elements. However the complement laws give the fundamental properties of the somewhat inverse-like unary operation of set complementation.

The preceding five pairs of laws: the commutative, associative, distributive, identity and complement laws, can be said to encompass all of set algebra, in the sense that every valid proposition in the algebra of sets can be derived from them.

http://en.wikipedia.org/wiki/Set_operations_(Boolean)

If you still fail to notice the analogy, then, what more can anyone say, hmmm?

I would completely agree with you if your goal was Reductio ad Absurdum, but now you seem to be serious about your conclusion in post #763 again. But I will assume that I misread you and we can leave it at that.

Exactly.

There is either faulty premise or faulty reasoning (or both) being employed in the omnipotence paradox. And I have plainly demonstrated the solution.