mathematical proof of god or no god?

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I'm interested in seeing some of this "mathematical proof of god", from a religiously neutral, non-partisan source, if anyone knows of such a link..... I wanna study this theory, I am questioning that a god might in fact exist, but that if one does, it's not the god of a religion, and it's definately NOT the tyrannical big brother god that religion preaches down peoples' throats. As I have ample reason to believe religion is little more than a control tool and a divider among people.
Yeah, so I'm asking if anyone knows of a source that discusses mathematical proofs of god without religious bias to one religion or another. Prefferably one that operates independent of religious limitations.

Closest I can think of is the ontological argument for the existence of god:
http://en.wikipedia.org/wiki/Ontological_argument

Formulated formally using model logic by Herr Goedel:

http://en.wikipedia.org/wiki/G%C3%B6del ... ical_proof

I do not know of any other "mathematical proofs" of God's existence

Do you know how I can translate that table?

lol! unfortunately, logic is hardly my forte. It could take me days to interpret the argument properly. It should approximate the argument form of Anselm's original ontological argument. I'll try to get an interpretation to you, but the wikipedia on it should tell you more than I could hope to.

Is there a logician in the house?

well, according to the article from wikipedia, the way I understand it, is that only shows a possibility, so it wouldn't be a 'proof' exactly, which it seems like that, as it follows the rules of logic, although as the article says, it uses modal logic, a possible truth rather than an absolute truth.

I don't understand the formuila though.

No, if there's one thing I can tell from that proof, it's that the modal operator in the conclusion is a must.

Unfortunately, less interesting than you'd think (unless you're familiar with Anselm's argument; then, like me, you will soon be rolling your eyes in disappointment)
As explained in wikipedia,
P(phi) is to say that phi is a "positive" property, which doesn't seem to have much of a meaning outside of this proof to me (but that's a whole 'nother mess)
G(x) is to basically say x is God. Here's my natural language translation

Axiom1: If something has one of these "positive" properties, then any property it has as a result of the first property, is also "positive"
Axiom2: If it's positive not to have a property, it's not positive to have it.
Theorem1: If a property is positive, it could be the case that something actually has this property
Definition1: x is God if and only if x posseses all positive properties
Axiom3: The property of being god is also positive
Theorem2: It might be the case that there is a god
Definition 2: a property is the essence of x if and only if x has that property and, given any other property x has, we can conclude that it is necessary (in all possible worlds) that for anything, if this thing has the first property then it has the second. This is the most confusing premise, but it basically seems to say that we call a property the essence of an object when it implies all other properties in all possible worlds.
Axiom4: a property being positive is not contingent, i.e. it must be positive in all possible worlds
Theorem 3: We can therefore conclude that if x is God, then godliness is the essence of x
Definition 3: x has the property "necessary existence" if and only if given any property, if this property is the essence of x we can conclude that it must be the case that there is some x with this property
Axiom5: necessary existence is a positive property.
Theorem4: thus, if x is God x posseses "necessary existence"
Conclusion: God must exist

Did that make it easier? No? Behold Saint Anselm: the patron saint of headaches.
The short of it:
There are good properties. One of these is "necessary existence". Something is called "God" if it has all good properties. Therefore, God possesses "necessary existence. Therefore, a non-existent God is a contradiction in terms.
I don't see as Goedel was able to give anything new to the argument other than a glossy logical sheen.

Last edited by twoshots on 03 Jan 2008, 2:02 am, edited 1 time in total.

I think you must be right

So most likely, that would be a must because of Necessity.
Interesting.

The nature of reality, including the existance of a higher power, can't be discovered through pure logic and/or mathematics, they are constructs that conceptualize reality into something understandable to our brains and thus are not sources of knowledge themselves but only tools used to understand empirical data.

The nature of reality cannot be understood by pure logic, merely because pure logic does not have premises, however, where is the proof that math and logic fail when premises do exist? Math and logic are frequently the tools of analysis after we get empirical data, and the extrapolations of truth from empirical data based upon math and logic are often true and this is verifiable with empirical data. The empirical data itself is a construct to conceptualize reality into understandable units so I don't see why it is *that* special. It is not as if we can have useful knowledge that isn't constructed into a logical theory to bring the specific to the general.

My thoughts exactly, except you worded them more intelligently than I could have.

Personally, I think that rationalizations of a god using strictly mathematics are mislead. Even among the physical sciences, it is not mathematics purely that solves problems, but within a scientific context.

Logic and Mathematics are necessary conclusions about any possible experience.




Being(God,or "one that is") as such posses necessary existence,since non-being does not exist.
Attributes of beings are changeable but being as such must always exist.

Non-existent God is contradiction in same manner as non-existing existence.



Logic and Mathematics gives necessity in their answers.Thats why most sciences use Mathematics and Logic as tool.



This topic is about mathematical proof of God or no God,not about empirical proof of God.

If one would give you logical arguments that God exist,you could always say that they are not empirical.But,if someone could give you empirical arguments for God,you could always say that they are not logical.



Mathematics and Logic are the most strict forms of thinking.



Yes,but 'God question' cannot be job of physical sciences,since job of physical sciences is researching of PHYSICALITY.
Idea of God is of higher logical and ontological level of pure physicality.

Emotions,Ideas,Morality..etc (as phenomenons) are not physical,yet they are real.

To use physical sciences to prove God is the same thing as using Chemistry to prove Music.



Goedel just analyzed Anselm's claim,and proved that this argument was properly logically formulated.Thats all.

I know, but by themselves, are they the most applicable?



Good point.

If we claim something to be rational and logical,then this something must be based on Logic and Mathematics.

Modal logic distinguishes between contingent truths and necessary truths, and this is what was used in the proof.




This is pure semantics, and I think Goedel's argument is better formulated than this. Goedel didn't say "a non-existent God is a contradiction in terms"; I was just trying to be concise. What he said is that the notion of "Godliness", together with the possibility that some thing possesses this property, implies the necessity of a satisfactory thing's existence. It is not so much "Nonexistent God is absurd" as "If it is not the case such that some x satisfies the property of Godliness, this is inconsistent with the definition of Godliness and is therefore absurd". Otherwise the argument is tantamount to saying "There must be an elephant on my head because a nonexistent elephant on my head is absurd", which is just plain silly.

I should also note that even the Ontological Argument can't really be called "pure logic" as it contains axioms which may or may not be true. It is, however, the best example of an a priori proof of God's existence.

This was not Goedel's argument,since he analyzed idea of God as subjective idea (at least its how Anselm formulated it).
I mostly said that concept of being(as such),implies necessary existence.
Since you used word 'must'...and I just wanted to show example how negation of one concept is contradictory.

As for semantics...basically entire language is semantics (and syntax).



Off course not.But if we say that God is being as such,then denial of its existence would be contradiction.



True.Similar argument was used by Gaunillo,to deny Anselm's arguments.

However 'Elephant' and 'Head' are individual categorical entities,while God even by medieval definitions is something that underlies ALL individual entities.
So using particular and temporary entities is not good example against something that is not an entity.



No one have said that Ontological argument is 'pure logic'.
Pure logic is strictly formal.