Does the set theory prove that there is no God?

In summary: 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.
  • #1
C0mmie
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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?
 
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  • #2
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
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
In short no. You can't prove such things using only logic.
 
  • #5
<<<GUILLE>>> said:
and the problem is that god and everything that hos to do with him, is the opposite of logic.

I am interested in the reasoning behind your claim. Please explain.
 
  • #6
wave said:
I am interested in the reasoning behind your claim. Please explain.

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.

but there are some contradictions...

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
<<<GUILLE>>> said:
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.

but there are some contradictions...

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.

I see what you mean now. Thanks. :smile:
 
  • #8
@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". Let's say youve never been there either. But let's say the kid was wrong with the coordinates of it by a long shot. Let's say you go to those coordinates and you find a cow eating grass... . no no, millions of cows eating grass just becauase its funnier to imagine :D... anyhow, that doesn't actually prove Manhatten doesn't 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 doesn't 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 there's a God!" or "hey, people can evolve, this means there's 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.
 
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  • #9
<<<GUILLE>>> said:
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.

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
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
C0mmie said:
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.

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
C0mmie said:
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?
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... :biggrin:
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!
 
  • #13
symplectic_manifold said:
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. :)

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 [tex]\sqrt {1- \frac {v^2} {c^2} } [/tex] there is no God? I don't get you...
 
  • #14
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
Hi every body.
Without having much knowledge of quantum theory or relativity theory, I am interested in knowing though, how exactly does this theory prove that there isn't a god?
 
  • #16
PhYsIcAlLy QuAnTuM said:
Hi every body.
Without having much knowledge of quantum theory or relativity theory, I am interested in knowing though, how exactly does this theory prove that there isn't a god?
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
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
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
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
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
loseyourname said:
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.
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
Jonny_trigonometry said:
Sometimes things are arbitrarily defined in mathematics. For example, the factorial of zero is defined to be one.
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).

Now by how a factorial is defined, you'de think that 0!=0, but mathamaticians say that it's not zero, but one.
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.

Just like how mathematicians say that there are no universal sets.
Do they really say this ? Please point me to one such mathematician.

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,
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!.

thus all math is wrong because it doesn't account for this.
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.

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.
 
  • #23
Gokul43201 said:
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 ...

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 apparent 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)."
 
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  • #24
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 existence of god.
 
  • #25
Jonny_trigonometry said:
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.

The definition can be generalized using the gamma function. Take a look at it and you'll see why 0! = 1.
 
  • #26
It has nothing to do with the definition of the factorial. It does have the property of what a "continuous factorial" would be when we chose to input real numbers. The gamma function doesn't define the factorial. this does:

n!=n*(n-1)*(n-2)*...*(1), 0!=1 (my fault for stopping at 2 earlier)

we defined it that way and it allows us to interpret the gamma function as a "continuous factorial" using real numbers. It just so happens that Gamma(x)=(x-1)Gamma(x-1), but this doesn't define the factorial for real numbers (because the factorial is already defined in the positive integers), although it does generalize what it would be like.

"for a real argument x, Gamma(x)=(x-1)Gamma(x-1)

If x is an integer n = 1, 2, 3, ..., then

Gamma(n)=(n-1)Gamma(n-1)=(n-2)(n-1)Gamma(n-2)=(n-1)(n-2)...1=(n-1)!

so the gamma function reduces to the factorial for a positive integer argument." - http://mathworld.wolfram.com/GammaFunction.html

Here, they are using the definition of the factorial as stated above, they didn't derive the definition of the factorial. It was defined the way it was so that it can be used in helping define functions like the gamma function.

if you use the definition n! with real numbers x, you get x!=Gamma(x+1), Gamma(0)=1. If x! wasn't defined the way it is, then x! could equal Gamma(x+1). The lim (as x approaches zero from the right) of Gamma(x+1) = 0 not 1. so the way the factorial is defined means it is discontinuous at zero so the extra constraint that Gamma(0) = 1 must be accounted for. All of this is based on if you were to define the factorial with Gamma using real numbers and allowing one integer downward into the negative reals approaching -1 as Gamma(x+1) approaches zero. If we don't allow an integer to be subtracted from x such that -1>x-1<0 (as when defining x!=Gamma(x+1), Gamma(0)=1 for reals), then x!'s domain changes from [0,infinity) to [1, infinity). In this conception the iterated stepping downwards an integer at a time stops when it reaches bottom, and bottom is zero, there is no more "stepping down" if you're at the bottom. Then the function is even more discontinuous, it's defined at 0 as 1, and defined from 1 to infinity, with a gap along 0>x>1. I plotted the x! function and the Gamma(x+1) in mathematica from x=0 to x=1.5 to be sure and saw no differance, they both approach zero comming from the right, between in the interval (0,1), x! is negative and concave up.

I guess the point is that we define functions and axioms according to our interpretation of them when we consider how they can fit together easier with other ones in an effort to render more powerful functions and axioms.

I've always interpreted zero to be nothing, but through this exploration I think that maybe it's the wrong interpretation (of course the word nothing may mean something different to you than to me). Rather, zero represents nothing and it is something. If this is how I should interpret zero, then I can treat it as an entity and I can add up how many of them I have, but it doesn't matter to me, because no matter how many I have the total value it represents is nothing. I guess I got to get over my distaste for treating zero as something rather than nothing.

I always figured that if I have nothing, then I can't put anything in any particular arrangement, so there are no combinations of arrangements of anything. But the factorial is defined as if there is a single possible arrangement of nothing. But what about two nothings? three? hehe...
 
  • #27
whoopse...
"I always figured that if I have nothing, then I can't put anything in any particular arrangement, so there are no combinations of arrangements of anything."

Should be...
"I always figured that if I have nothing, then I can't put anything in any particular arrangement, so there are no combinations of arrangements of nothing."
 
  • #28
Thanks Goku|34201 and Wave, for helping clear up my main problem of my interpretation of zero as being nothing rather than representing nothing and at the same time is something. I think that's how it's suposed to be thought of. I don't understand how a set of zeros means anything more than zero, but I just got to accept it I guess. Maybe I'll understand later.
 
  • #29
Jonny_trigonometry said:
I've always interpreted zero to be nothing, but through this exploration I think that maybe it's the wrong interpretation (of course the word nothing may mean something different to you than to me). Rather, zero represents nothing and it is something. If this is how I should interpret zero, then I can treat it as an entity and I can add up how many of them I have, but it doesn't matter to me, because no matter how many I have the total value it represents is nothing. I guess I got to get over my distaste for treating zero as something rather than nothing.

I always figured that if I have nothing, then I can't put anything in any particular arrangement, so there are no combinations of arrangements of anything. But the factorial is defined as if there is a single possible arrangement of nothing. But what about two nothings? three? hehe...

Consider the empty set. There is exactly one way to arrange zero objects. Thus 0! = 1 is consistent with the combinatorial interpretation of factorials.
 
  • #30
There is only one way to arrange 1 object because 1!=1. So I guess I should think of zero as an object...
 
  • #31
zero is served to us by one ''finite description''

zero is served to us by one ''finite description'' within which we find that it excludes the posibilty of ''something'' existing.
these descriptions are absurd.
this is because we are always dealing with ''uniques''.
lets see one example for uniques, one apple which is not the same as the next apple less this next apple is our first apple with our next apple somewhere else.
it is not empty or nothing or zero.
one is one ''something'' because we have defined that one ''something''.
there exist a limit to definitions though.
we will always be able to find the diference between one apple to the next.
the same as one particle to the next etc.
usually coordinate diferences and time diferences are those that will give us the final diference.
size , colour , shape etc are the first ones we usually use.
even our original apple is never the same as itself, never!.
no statement or affirmation or description can give us zero.
imagine that we tried eliminating all of these ''uniques'' descriptively to try and obtain a cosmic empty.
we cannot.
i proposed to myself developing something called the nexo theory...
and i came up with what i called in spanish ''lazos o franjas'' which are like ''ties or gaps''.
the idea was to reduce the diferences to have a minimum gap or a very short tie.
this would start us off with our nexo relationships.
''something'' then didn't have to be the same as something else , only aproximately or be related!
and graphically nexo lines do not cross at a ''zero''.
its not like x, y and z lines.
infact they do not cross.
there is always a volumetric overlapping or sharing.
but its never a total overlap or share.

i'm flying and at this moment i don't need an undercarriage...maybe a north!
 
  • #32
I don't think anything we have or do can disprove god. Our minds arent equipped to do that, we can understand if he exists or not if its said to us and is the truth, but our minds are not smart enough to disprove him right now with what we have. Someday, maybe, but for the next few decades and probably centuries, heck no. Wed have to find out if other universes exist and visit them and also explore every millimeter of our universe and every other universe, wed have to have a way to commit suicide and come back to explore afterlife and numerous other things.
 
  • #33
There's always new discoveries on this topic. Ton's of myths, rumours, notions.
No-one really knows till you experience it, right? All I know is if God is going to be a hardass and send me to hell for smoking and "ruining his temple" or stealing from some guy a hate, but completely miss the fact that I'm generally a good person. Then he can go to hell with me.
Play around with the fact that there's so much room for opinions when talking about an after-life. The insecurity of the subject makes the struggle to prove anything kind of pointless.
 
  • #34
Pengwuino said:
@GUILLE

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.

On the other hand, just because we know how the seasons change doesn't mean that it isn't God's will.
 
  • #35
C0mmie said:
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?

Both God and universe are constructions of mind, which are not objectively related. There is no objective existence definable for them.
 

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