Mathematical Argument For The Existence Of God

1. Nov 24, 2003

Russell E. Rierson

This is an interpretation of Christopher Langan's CTMU, www.ctmu.org , and Saint Anslem's ontological argument.

1.] If it is possible for a mind to perfectly understand[model] every aspect and detail of reality, then the mind that perfectly models reality is a super-intelligence, for all intents and purposes, the super-intelligence is God.

2.]If the perfect correspondence can be approached via a convergent analytic-synthetic propositional "limit", then the limit exists, even though a sentient mind within reality can only approach the limit.

3.] If the limit exists, the exact mental correspondence exists in the mind of a super-intelligence.

4.] That is to say, if the limit exists then a description exists.

5.] If the description exists then the "describer" exists, since the description is isomorphic.

6.]The describer is a super-intelligence.

7.] By definition, the super-intelligence is God.

The burden of proof becomes the burden of proving the "convergence", to an exact correspondence, between the mental construct[infinite number of axioms] and reality

At the limit

[MIND]<--->[REALITY]

M = R

[axiomatic method]--->[exact correspondence]<---[scientific method]

2. Nov 24, 2003

FZ+

This, as common to all ontological arguments, is a flaw. Not many people agree with a god in terms of omniscience only. In fact, QM suggests that any such omniscience is logically invalid.

But this limit is only a conceptual limit from our understanding of universal logic, from a source which you have admitted that we being sentient is imperfect.

Can you clarify this? The conclusion to me seems different: If the limit exists and the super-intelligence exists, then a description exists. Which would make this a circular argument.

3. Nov 24, 2003

phoenixthoth

what's wrong with this "argument?"

let T' be T combined with the trait of existence if not already in T.

define God to be a being with every trait in T'.

therefore, God exists and has all traits in T.

4. Nov 24, 2003

Russell E. Rierson

UPDATE:

1.] If it is possible for a mind to perfectly understand[model] every aspect and detail of reality, then the mind that perfectly models reality is a super-intelligence, for all intents and purposes, the super-intelligence is God.[ This is self evident. No human[sub-sentient] mind will ever be able to know every aspect and detail of the universe from its beginning to its ending. We are the products of a creator, we are not "the" Creator.]

2.]If the perfect correspondence can be approached via a convergent analytic-synthetic propositional "limit", then the limit exists, even though a sentient mind within reality can only approach the limit.
[ All that needs to be proven is that the limit converges. No "sub-sentient" mind within creation itself can know every aspect of ...creation itself.]

3.] If the limit exists, the exact mental correspondence exists in the mind of a super-intelligence.
[self evident]

4.] That is to say, if the limit exists then a description exists.
[another way of stating 3.]

5.] If the description exists then the "describer" exists, since the description is "isomorphic"[ one to one and onto].

6.]The describer is a super-intelligence.

7.] By definition, the super-intelligence is God.

The burden of proof becomes the burden of proving the "convergence", to an exact correspondence, between the mental construct[infinite number of axioms] and reality

At the limit

[MIND]<--->[REALITY]

M = R

[axiomatic method]--->[exact correspondence]<---[scientific method]

5. Nov 25, 2003

FZ+

This still doesn't seem to confront the core of my complaint:

To me, all this seems to be saying is that, by analogy:

Because successively more accurate measurements can be made of a value, towards a limit which is the "real" value, there must exist an infinitely accurate measuring instrument by which the real value is contained.

But this argument is absurd, and to make sense of it, we must modify it into:

Because successively more accurate measurements can be made of a value, towards a limit which is the "real" value, IF there exists an infinitely accurate instrument, the real value is contained within it.

So the arguments as to whether this real limiting value exists is a diversion from the core flaw - that this is a circular argument.

6. Dec 20, 2003

Russell E. Rierson

[ abstract representation]---[semantic mapping]--->[represented system]

The abstract representation cannot be an "exact" semantic mapping with the physical system, since every nuance, or aspect, of the represented physical system cannot be observed. Is it possible to explain the exact semantic mapping as a converging limit, or converging series of axioms, that is approached but never reached?

The burden of proof would then be to "prove" that the limit is converging.

X is an analytic proposition, then proceed with the a deductive process of deriving axioms, utilizing rules of logic.

Then in the opposite direction, start with the scientific method, utilizing an inductive limit:

Two converging limits, that intersect at infinity.

[axiomatic]---->[represented system]<----[inductive]

1.] If it is possible for a mind to perfectly understand[model] every aspect of reality, then the mind that perfectly models reality is a super-intelligence, for all intents and purposes, the super-intelligence is God.

2.]If the perfect correspondence can be approached via a convergent analytic-synthetic propositional "limit", then the limit exists.

3.] If the limit exists, the exact mental correspondence exists in the mind of a super-intelligence.

7. Dec 20, 2003

phoenixthoth

i think "God exists" is an axiom xor a nonaxiom.

8. Dec 20, 2003

Sikz

I don't understand where you people are coming from with this one- I hear it repeatedly. I soppose you mean that QM renders some things unknowable because they are actually random. Since it is unknowable, you reason, no omniscient being can exist.

But... QM is physics. What it says does not apply to a god. In fact doesn't it argue FOR one more than against one? If there was no "random", "unknowable" element we would be able to predict everything. If we could predict everything then it is all preditermined and there is no way for any "supernatural" force to effect things (since everything is predictable by the laws of physics). QM gets RID of this barrier, it doesn't introduce a new one. It isn't actually unkowable- just underivable. What I mean is that there is no way to solve for these "random" things based on any other events. That means you cannot derive the knowlege- it doesn't mean the knowlege doesn't exist independent from the other facts.

Also, I really don't get what the proof is sopposed to prove. All it actually says is "If everything has a true value, the being that knows these values is all-knowing. We will call it God."
Uh... why? The existence of something does not prove there is an exact model of it elsewhere. Your proof hinges on this:

1.] If it is possible for a mind to perfectly understand[model] every aspect and detail of reality, then the mind that perfectly models reality is a super-intelligence, for all intents and purposes, the super-intelligence is God.

In fact that contains the entire proof- and it isn't a proof at all but an unfounded assumption. It says "If there is a mind that can know everything, there must be a mind that knows everything. Let's call it God." So your main axiom for proving God's existance is "God exists". That is excellently illustrated here:

3.] If the limit exists, the exact mental correspondence exists in the mind of a super-intelligence.

Again I ask you, "Why should there be a correspondence?". Your proof is FOR the corresponding model, yet dependent upon the corresponding model's existance. Imagine that there is no model in some mind of a being corresponding to reality and read your proof again. Why can't the instrument that measures this ultimate reality be the universe itself? There is no need to introduce some exterior model... Even if I don't have a picture of a particular apple it still exists- the "value" of the apple is contained in the apple itself, a perfect likeness of it is not necessary for it to have a value.

By the way, if the omniscient superintelligence has a perfect model of everything, it cannot exist:

1) An omniscient being must have a model of all reality.

2) If an omniscient being exists, it is part of reality.

3) An omniscient being must have a perfect model of itself.

4) The model, being perfect, must have a complete model of all reality, including a self-model with the same knowlege. This goes on infinitely.

So we have a paradox... No perfect model can ever contain the whole of reality, because it will always have to contain itself. If it doesn't contain the whole of reality it is not perfect.

Interesting, eh?

EDIT: It cannot exist, that is, unless it in its entirety IS reality itself. :)

Last edited: Dec 20, 2003
9. Dec 20, 2003

Russell E. Rierson

All that needs to be proved is that the limit is converging, but that may be more difficult than it sounds. If the limit is converging, the universe is a "mind".

10. Dec 20, 2003

Russell E. Rierson

Existence is a definition, a predication, which is why Kant so vehemently denied that existence is a predicate, but alas, existence is a definitive constraint as is all definitions. To exist means "to be". So infinite paradox becomes infinite freedom from constraint, and reality itself is an infinitesimal difference, from perfect equilibrium.

The "Ein Sof" is an infinity that cannot be comprehended. For every set A there is a choice function, f, such that for any non-empty sub set B of A, f(B) is a member of B, and so we see that there may be an infinite number of sets B within A, and as such the Banach-Tarski paradox is created. A single sphere is decomposed and re-assembled into two spheres, each with the same radius as the original sphere.

So we see that:

therefore:

is absolutely true.

Alpha = Omega

It is the categorical formulation of the simultaneous, situational, instantiated contradiction, where deductive invalidity is the product of the utmost categorical truth of the assumption that if the antecedent of a true conditional is false, then the consequent of the conditional is true or false indifferently, and of the categorical falsehood of the conclusion condequently predicates that if it be not the case that the consequent of a true conditional is true or false indifferently, then, it is not the case that the antecedent of the conditional is false. To pronounce the consequent of a true conditional as being true or false indifferently is tantamount to saying modally that where the antecedent of a true conditional is notoriously false, then the consequent can, or could be, or is possibly true or false. But it may be worthwhile to see that the definitive, simultaneous equality of both true, and false, can be formulated without explicitly including modal terms, which become the predicating operators, which, for the sake of showing that the consequent paradoxical conundrum is not straightforwardly resolvable by appealing to concrete philosophical scruples concerning the intensionality of predicated modal contexts.

The categorical representation of the propositional anti-logic, in which deductive invalidity depends on the modality of the truth conditionals concerning the prerequisite of the contingent assumption and consequent conclusion. The totally relevant content of the assumption and conclusion, definitely contains no modal terms. But, the modality attaches to the fact that the conditional assumption is quite possibly true, while the conditional conclusion is necessarily false.

Which leads us to an argumentational representation of a completely non-bogus modal formulation of the "paradox". Deductive invalidity is most excellently predicated on the categorical truth of the modal-term-laden assumption and the definitive categorical falsehood of the modal-term-laden conclusion. Hence, the assumption is such, that if the antecedent of a contingently true conditional is false, then, the consequent of the conclusion can be true is itself quite simply, ...true. Therefore, the conclusion that if it is not the case that the consequent of a contingently true conditional can be true, then it is not the case that the antecedent of the true conditional is false, is itself quite simply, false.

Meta-philosophical scruples notwithstanding, existence is, a paradox, albeit a dynamic self resolving one.

.
To exist means "TO BE" is a first principle which is an absolute, or what is synonymous here, an abstract beginning; that does not presuppose anything, it is not be mediated by anything which means that it is the ontological substrate for the whole "she-bang". It does not have a basis; rather it is to be itself the basis of the entirety of existence itself. The Total Existensial Entity called God. Consequently, it must be purely and simply an immediacy, an absolute necessity, or rather, merely immediacy itself. Just as it cannot possess any determination relatively to anything else, so too it cannot contain within itself any determination, any content, for any such would be a distinguishing and an interrelationship of distinct moments, and consequently a mediation. The beginning therefore is "Pure Being."

Alas, to state that reality is Being seems to be to say nothing specific about reality at all! The concept of Being is an empty concept, whose content is nothing. Yet the concept, that of Nothing, which has equivalently, the same content as the concept of Being, but which seems to stand in diametric opposition to it. Nothingness is . . . the same determination, or rather, an abscence of determination, and thus altogether the same as, the pure essence of being. On the other hand, paradoxically, Being and Nothing are not the same. So we have the difference of Being and Nothing passing into identity, and the identity passing into difference. Ergo, their truth is, this movement of the immediate vanishing of one in the other: becoming, a movement in which both are distinguished, but by a difference which has equally immediately resolved itself. A self resolving paradox. The new concept is generated by the "sublation" of the first two. This process of generating a third concept as expressing the identity and difference of the first two is fundamental to the discipline of logic.

11. Dec 21, 2003

Yahweh

If you define something as "omniscient", then it doesnt exist. The reasoning behind this is the fact to be omniscient, you must know everything, including that which you do not know: And a fatal error, a logical contradiction.

If God is super-intelligence (or omniscient), then he does not exist.

Here is the proper annotation of why omniscience is a logical contradiction:

The original claim is that the god is super-intelligent or omniscient, omniscience itself fails this test. To know everything, you must know about that which you do not know -- which is a logical contradiction.

To illustrate the point, consider: God1 creates God2 in such a way that God2 believes he has all of the powers, capabilities, and possibilities as God1 -- such as always having existed, controlling the rules and specifics of his own universe, etc. Additionally, God1 creates God2's reality in such a way that God2 does not know that God1 and God1's reality exist -- and cannot know, unless God1 deems to reveal this to God2.

Now, consider: Can God1 know that he is not also in the same position as God2. Could a God0 exist that God1 does not know about? If he cannot answer this question, he cannot claim to know everything. He has an unresolvable blind-spot in his knowledge and is therefore DEFINITELY NOT OMNISCIENT.

By this, if super-intelligence is God, God does not exist.

12. Dec 21, 2003

phoenixthoth

assuming all your premises are right, you might want to check out the discussion on "russell's paradox: the achilles heal of solipsism" which is about similar ideas. it's under the logic section of phil.

by contain itself, do you mean a kind of proper containment (like an element of) or as a subset of? every set is a subset of itself.

russell's paradox rules out a universal set which would contain itself in both senses. however, 3 valued logic rules out russell's argument. hence, unless there are differently structured paradoxes that 3 valued logic (and/or fuzzy logic) can't rule out, the universal set can exist.

in max tegmark's article on the TOE, he posits the existence of self-aware structures and if U is such a structure, since it contains all manifolds, it would be, in a sense, omniscient.

one esthetic objection to living in a set is that it's static yet we seem to be moving around. U has a dual nature of being static and dynamic, depending on your point of view, not unlike the dual nature of things that are really small.

consider f(x)=x^2. is it constant or not?

well, it's derivative is not always vanishing and it's not a constant function.

however, f={(0,0),(1,1),(2,4),...} is constant. it never changes.

so f is somehow alive and dead all at once. the duality somehow passes into unity in U and the unity includes duality.