# Does the set theory prove that there is no God?

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 gotta 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...

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."

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 thats 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 gotta accept it I guess. Maybe I'll understand later.

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 gotta 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.

There is only one way to arrange 1 object because 1!=1. So I guess I should think of zero as an object...

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!

I dont 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.

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 theres 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.

@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.

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.

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.
I'm not sure on my feet in a philosophical discussion. But being omnipresent is not the same thing as being a universal set. Can you make your question more precise?

I'm not sure the various omni's used to define G-d are meaningful. To say that something is 'everything' goes against the etymology of the word 'define'. It brings me to mind of a high-school dropout looking for that first job:

HR: What can you do?
Kid: I can do anything.
HR: Right now we're not looking to hire a person that can do 'anything'. We need a person that can do 'something'.
Kid: I can do something.
HR: What can you do?

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Both God and universe are constructions of mind, which are not objectively related. There is no objective existence definable for them.
I'm not sure what you're saying here.

I'm not sure what you're saying here.
An objective relation means:
The apple I can see and smell and touch is a seperate reality, different and outside and apart of me. I am something different then the apple.
The apple is an object to me, and I am an object to the apple.
Me and the apple are objectively related.

Both God (before creation of the world, he was the sole and unique being) and the whole universe, don't have objects strictly outside of themselves, so they are not objectively related.
They can only be known subjectively.

@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?

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.

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.
Excellent... These words of yours have to be written on gold :)

Pengwuino,

What if the agrument is that God him self has said so? i.e. if God says "You are all guilty of sin and the punishment of sin is hell." Or reather, is your argument still true if:
1) God says it.
2) Someone repeats what God says.
3) Someone says "God says..".
4) Someone presumes what God wants.

And I am sure there could be many more levels inbetween thoughs 4 and beyond, but I see no need to try to add them all. One things very evident from this and other threads though; God will never be proven or disproven (at least as we exist now.

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?
Since when is God a set or an quadrant system?

One things very evident from this and other threads though; God will never be proven or disproven (at least as we exist now.
In the same way a thought or a feeling will never be proven or disproven. But hold on a sec...

In the same way a thought or a feeling will never be proven or disproven. But hold on a sec...
or in the way a non-falsifiable/verifiable claim can be proven...

Have you tried to prove that you are sane with out appealing to your sanity? Have you tried proving that Bigfoot DNE without being everywhere at once?

I tried to read trough the tread, but I can not see that you define anywhere abouve what a God is. Neither I can see that you define what the word exist does mean.

How can it be possible to conclude positive or negative if something unknown has an uknown condition ?

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?
This is not exactly true. Contradiction would exist if there were no 'Continuous Set' (that is, a set that eats up all contradictions), and God were not the owner of this set. Since Continuous set exists and God owns it, there is no contradiction. Just think about it for a moment.

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?
Short answer no. Here's a few thoughts on the matter though:

God being omnipresent usually means that God is witness, aware, part of to all things. So the Set God = {All beings who are aware of all things} or {... occupy all positions} or possibly {...are a component of all things} (assume there is one member of this set, if you like, i think this set is empty personally; but that's another topic) Anyway sets can contain other sets, so set Apple = {material components of apple, God} this would imply that God is a member of all sets, rather than a set of all things.

If you are saying that all things are "part of God" then there is still no problem as God is Itself not part of this set. So set God = {everything but God}. (note that saying that all things are part of God is very different than saying that God is part of everything)

Or you could redefine God=Universe (in the set theory sense, that is everything that can be in a particular set or not) which is still not a violation of set theory. In fact set theory usually requires that you define a "Universe" prior to getting on with your set defining.

Alternatively you could interpret the axiom of set theory you mentioned as stating that: "Set theory only applies to constructions that do not include a universal set"

The answer though really is that the concept of God is intentionally constructed in such a way as to make it impervious to logic. God is generally defined more or less as that being to which rules don't apply.

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Even in set theory not everything is a set. Try Googling "proper class"

CRGreathouse
Homework Helper
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?
I interpret omnipresent differently, but using your definition as a base, couldn't omnipresent mean that God is the class of all sets? This is allowed in most axiomatic theories. What part of omnipresent requires it to be a set and not a class?

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

Perhaps only through subjectivity could one come near to God. It is faith. Objectifying the definition of God seems to be a dilemma of modern philosophy. There are a lot of questions upon Cosmology which we shall try to answer, and shall never be able to answer at all. We cannot even use any imperical method to prove "Love".

It seems that the so-called Logic which humans all try to embalm may somedays expand as we breakthrough the universe by our technology. But what could say about God existence is "unknown". It is a sort of similar to that the thought of "x" does not exist does not mean the existence of "x" has no evidence.