Does the set theory prove that there is no God?

1. Apr 23, 2005

C0mmie

One of the axioms of the axiomatic set theory is that there are no universal sets. However, God is omnipresent, so he would have to be this universal set. Thus, God would immediately lead to a contradiction within the set theory. Does this prove that there is no God?

2. Apr 23, 2005

symplectic_manifold

Well, to bring it further, one could also say that the absence of God was already proved in physics by Einstein's Theory of Relativity, which showed that there are no universal coordinates or that the universe has no centre.
I'm not sure we could prove or disprove the existence of God, or reveal contradictions within the concept itself and claim our deductions to be appropriate, using the human-made tools of thought like mathematics or physics. There is more to this term than we can imagine.
I personally believe the concept "God" should be treated in psychological terms.
But there is more to say on this topic, I believe. :)

3. Apr 23, 2005

<<<GUILLE>>>

the fact is that set theory and many other things used in philosophy are based on logic. and the problem is that god and everything that hos to do with him, is the opposite of logic.

4. Apr 23, 2005

Vega

In short no. You can't prove such things using only logic.

5. Apr 23, 2005

wave

6. Apr 23, 2005

<<<GUILLE>>>

ok, what I tried to say is that god and the idea of him leads to many contradictions.

For example, believers say that god doesn'y control our life and let's us deside the way we want.

1) if you don't follow god's way, and your an atheist or another god beleiver, then you will go to "heil" so, god is deciding what will happen to you.

2) they also say that god nows it all. If he has gone to the future and nows that I will be an atheist (already are) it isn't what I decide to do, but what he has seen. inverse history.

7. Apr 23, 2005

wave

I see what you mean now. Thanks.

8. Apr 23, 2005

Pengwuino

@GUILLE

Problem is though is that everything that is based on an argument of a God is said in the words of people. The thing is, when you say "they say you will go to hell", how are "they" to know what God does? To put it this way...

A kid whos never been to Manhatten says "Manhatten exists and is at such adn such lattitude, such and such longitute". Lets say youve never been there either. But lets say the kid was wrong with the coordinates of it by a long shot. Lets say you go to those coordinates and you find a cow eating grass... . no no, millions of cows eating grass jsut becauase its funnier to imagine :D... anyhow, that doesnt actually prove Manhatten doesnt exist simply because one person gave you the wrong directions.

Whos to really say God gave us free will? Just because some person said so doesnt really make it so. Its like trying to explain an experiments results without you ever having done the experiment (nor anyone else ever having done it). Does god know the future? Who says he does? How do you know they have any evidence that he does?

The real problem comes from the fact that your trying to in a scientific sense, contradict someone elses data from an experiment that they never really did.

I think what many people unfortunately do is have a personal opinion in their mind, and then they go out and look for evidence to support their own answer instead of how normal people do it who do things the other way around.

Its like some people who go "oh there was a big bang! it must mean theres a God!" or "hey, people can evolve, this means theres no God!". Theres various leaps of logic people tend to make way too often that turn this whole science vs. religion thing into a big ugly mess of crap. The people who said Seasons must be God's will at work were just as wrong as the people who now say darvin proved there is no God.

Last edited: Apr 23, 2005
9. Apr 23, 2005

C0mmie

Does religion not implicitly rely on logic?

If you sin, then you go to hell.
If the bible says to do x, and you do not do x, the you are violating the bible.

It is my understanding that theologists have to rely on logic to study religion, just as much as physicists rely on logic to study the physical world, the only difference is they start with different premises.

10. Apr 26, 2005

Artermis

I don't think you can "logic" your way to proving that there is no God.
Why can't God just simply exist in a higher dimension or a higher state of being that transcends human grasping, reasining, and thus, logic?
Philosophers themselves are divided over the issue of God, first year Philosophy will explain a lot of flawed reasoning behind some attempts to "logically" define out a God. (The original mover, ever-existence, etc...)

11. Apr 27, 2005

<<<GUILLE>>>

no, that part of religion, is only the thic-moral part. which tries to dogmatise morals etics and logics, dogmatising life.

for pengwuino (sorry if I didn't wirte it correcrtly),
of course they can be wrong in a few coordinates but it is in many times that it happens, and they never agree between the religions (or very little).

thirdly, just to describe god, I will write some words to see if you all think they are correct to describe him, which is actually the first thing we should do: infinity, perfection, completeness, loveness, eternity, creator...and others.

12. Apr 27, 2005

EvLer

Without having much background in axiomatic set theory,
I can see a different take on this: if you say that God is a set in some sense, you are saying that He is finite, which is a proof in favor of God's existence, because He is infinite (He was before the world was created and always will be, according to the Bible). So, there is no contradiction, at least in the way He presents Himself in the scriptures: God could be not defined in terms of finite entitity. That what sets Him apart as God. Duh...
Another more striking enigma that defies every mathematical/logical precept (although I did not investigate it in mathematical terms) is Trinity: God is one, but He is three! :surprised

13. Apr 28, 2005

eNathan

Explain this? The concept of god is that there is an allmighty being that is behind all that exists. Nothing can disprove that there is a god, not even the knowledge that things are relative. Because $$\sqrt {1- \frac {v^2} {c^2} }$$ there is no God? I dont get you...

14. Apr 29, 2005

loseyourname

Staff Emeritus
You cannot verify or falsify an empirical claim using a formal system of relations between abstract entities unless you can show the claim to be inconsistent. The best you can do is demonstrate the weakness or invalidity of certain arguments for God's existence, because the simple claim that God exists is not a contradiction.

15. Apr 30, 2005

PhYsIcAlLy QuAnTuM

Hi every body.
Without having much knowledge of quantum theory or relativity theory, im interested in knowing though, how exactly does this theory prove that there isn't a god?

16. May 4, 2005

honestrosewater

It doesn't. loseyourname explained this well in the post above yours.
The interpretation given doesn't really make sense anyway. An omnipresent object would most naturally be interpreted as a set which is a member of every set or possibly a subset of every set. But this isn't set theory, just as saying "What if we interpret a set as a horse..." isn't set theory. There are no horses or gods in set theory; The only objects in set theory are sets (or, at least, in most versions of set theory- some distinguish individuals and sets, but I've never seen one with horses or gods- and anyway, objects in set theory are still abstract objects).

17. May 5, 2005

loz

How exactly would you go about proving that God does not exist when God is said to be immeasurable. Only from the standpoint of absolute knowledge and understanding of everything in the universe and their relationships to one another would it be possible to "filter out" each part of the equation to be left with nothing. It seems that to disprove God you have to be God yourself.

18. May 5, 2005

Burnsys

I think that if logic does not apply to god, then it's irrelevant to us.... Becouse absolutly everything that we can feel. see, touch, ear, think ,etc, is governed by logic.. we will never "experience god". He would have no power to change anything, at leats in our "Logical universe"...
God can't violate law of conservation of energy, nor the gravity constant.... etc.....

19. May 5, 2005

arildno

This is basically a meaningless issue.
You cannot prove whether something is consistent or inconsistent with the axioms of set theory unless you assign properties to that something the collection of which then "is" your something.
Whose to say that how you CHOOSE to define God is the proper way of defining God?

The only thing you could hope of proving or disproving with set theory is some particular conception of God specific enough to make the question decidable.

20. May 6, 2005

Jonny_trigonometry

Sometimes things are arbitrarily defined in mathematics. For example, the factorial of zero is defined to be one. Now by how a factorial is defined, you'de think that 0!=0, but mathamaticians say that it's not zero, but one. Just like how mathematicians say that there are no universal sets. When we say that the factorial of zero is one, a person can take that statement to mean that zeros are ones and ones are zeros, thus all math is wrong because it doesn't account for this. A person may take the statement "there are no universal sets" and say that god doesn't exist.

21. May 6, 2005

Gokul43201

Staff Emeritus
However, it is hard to find an axiomatic system where things like omnipotence and omnipresence do not lead to internal inconsistency. Nevertheless, the "logical believers" do not seem to consider this a problem...nor have I heard anyone construct a working system. I wonder why ...

22. May 6, 2005

Gokul43201

Staff Emeritus
This is hardly arbitrary. It could have been an arbitrary choice, but it was more : it was a useful choice. It allows one to expand the factorial beyond the naturals (see the gamma function).

You would think that 0! = 0, only if you did not know the definition of a factorial. Besides, if you chose to extend the factorial from the naturals to the whole numbers and used "your" definition of 0!, then it would either (i) make all factorials = 0, by the obvious extension of the definition to suit your final step in the recursion, or (ii) omitting that extension, would still make problems like requiring C(n,k) diverge to infinity for n=k.

Do they really say this ? Please point me to one such mathematician.

The person can also take it to mean that horses are spherical and that pigs have wings; but that doesn't make it a logical consequence of the definition of 0!.

For "this" ? What is "this" ? "This" is a person who is misapplying mathematical definitions. Math does not account for human frailty, but that does not make it wrong.

He may also take that statement, add salt and pepper, and have it for breakfast.

23. May 6, 2005

Les Sleeth

That's correct, at least with the concept of omnipotence (omnipresense is a little different because if one were in touch with some consciousness behind all apparant reality, and everywhere one went one felt in the presence of this consciousness, then there is some justification for proposing it is omnipresent). Omnipotence is not supported by evidence, but instead is a praising speculation of theologians. If something is infinitely powerful, how could that be measured? I've argued in other threads that omnipotence isn't logically indicated, nor is omniscience or the creator being infinite and having always existed.

Just considering the logic of a creator (i.e., not whether one actually exists or not) I've said:

"The problem for the concepts of an omniscient, omnipotent, and forever existing creator is that evolution seems experimental and imperfect.

"The vast majority of species to ever have lived are now extinct evidently because they were unable to develop in ways that permitted their survival. It seems like an all-powerful creator who has forever existed would know everything, just as theologians propose.

"But then, how do we reconcile an all-knowing and all-powerful creator with one who creates countless species unable to survive? Or what about a creator who, considering how diseases and molecular freakishness (like destructive mutation and viruses) bring down life, seemingly creates less than perfectly (plus many of us wonder about certain members of the human race)? Wouldn’t an omniscient-omnipotent creator already understand exactly what to do, unerringly create a flawless creation, and be powerful enough to ensure things went perfectly?

"But if, on the other hand, the creator experiments, then it seems the creator is not omniscient-omnipotent, but is more likely an evolving creator. With the concept of an evolving creator we can reason that if the creator is becoming more evolved, then before the creator became more evolved the creator was less evolved. And tracing that process back we see there must have been a condition when the creator was un-evolved, which indicates there was an event which gave birth to the creator.

"That would mean any creator has not eternally existed (but, of course, it may continue eternally), cannot be omniscient, and needn’t be all-powerful (logically the creator needs only to be powerful enough to produce creation)."

Last edited: May 6, 2005
24. May 7, 2005

Jonny_trigonometry

what I was trying to point out is that the factorial function is defined as:

n!=n*(n-1)*(n-2)*...*(2), 0!=1

and not simply n!=n*(n-1)*(n-2)*...*(2).

the extra 0!=1 gives the factorial function more versitility.

Iwas responding to this statement:

"One of the axioms of the axiomatic set theory is that there are no universal sets. However, God is omnipresent, so he would have to be this universal set. Thus, God would immediately lead to a contradiction within the set theory. Does this prove that there is no God?"

And I wanted to point out that this particular axiom in axiomatic set theory (there are no universal sets), could simply be a definition that allows more versitility in set theory.

" A person may take the statement "there are no universal sets" and say that god doesn't exist.
He may also take that statement, add salt and pepper, and have it for breakfast."

so in essence we agree. If a person wants to they can think whatever they want about a mathematical statement, but any axiom or function in math only exists in math, and is independant of the real world. So my answer is no, such an axiom in set theory doesn't disprove the existance of god.

25. May 7, 2005

wave

The definition can be generalized using the gamma function. Take a look at it and you'll see why 0! = 1.