The logic of Kurt Godel

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• In the history of the universe we also see the introduction of information, some 3.8 billion years ago. It came in the form of the Genetic code, which is symbolic and immaterial.
  
• The information had to come from the outside, since information is not known to be an inherent property of matter, energy, space or time.
  
• Therefore whatever is outside the largest circle is a "conscious being "Maybe even God?".
  
• That is my point
  

You are taking quite the leap of faith. Nothing of Godel's suggests that what is outside of the largest circle is a "conscious being."

"I am a theist but hopefully a reasoning theorist (Alan Comment)"









modal logic, a branch of logic that was familiar to the medieval scholastics, and axiomatized by C. I. Lewis (not to be confused with C. S. Lewis, or C. Day Lewis for that matter).

It turns out that modal logic is not only a useful language in which to discuss God, it is also a useful language for proof theory, the study of what can and cannot be proved in mathematical systems of deduction. Issues of completeness of mathematical systems, the independence of axioms from other axioms, and issue of the consistency of formal mathematical systems are all part of proof theory.

Talking about proof theory often feels like discourse about God:

• When you talk about God, you have to discuss issues like "if God created the Universe, then who created God?" In proof theory you have to discuss issues like "if a statement is true, then is it true that we can prove the statement?" There is a bit of a feeling that we are arguing by pulling ourselves up by our own bootstraps.
  
• In metaphysics, one discusses the possible existence of counterfactual worlds in which God does not exist. In proof theory, one examines the independence of an axiom by finding models in which the axiom fails.
  
• In metaphysics, one can speak of "modal collapse" in which any proposition which is true at all is necessarily true. In proof theory can speak of "completeness" in which every statement which can be consistently added to the axiom system can be proved from the other axioms.
  

"The universe begins to look more like a "great thought" than a "great machine"

James Jean Astronomer

Is this philosophy of religion, or religious philosophy?



I wonder... . . .



:intentive:

I realize that the intended audience for this is the general reader and the general reader is not really ready for some of the technical stuff. However, there are too many statements like this out there that skip over the technical aspects of the proof and go straight to the grand pronouncements of what the proof means to life, the universe and everything in it. The same thing happens with some of the ideas of quantum physics.

What we need more of are expositions that make the technical matter of the proof understandable and entertaining to the general reader to the extent that this is possible. This will make the grand pronouncements all the more convincing and thus all the more shocking and intriguing.

Whenever possible the effort should be made to not simply refer to the authority of geniuses and the class of experts who have given them the stamp of approval.

That said I don't think I am up to the task that I'm recommending you try.

Also you might check out what the psychoanalyst Lacan made of Godels proof. Lacan made some grand pronouncements that are worth adding to the list.

That there are undecidable propositions within a deductive system is self evident given the axioms of that system.
All axioms are undecidable within the system that uses them.

When an axiom is decided true, it then becomes a theorem of that same system.

If we have an unprovable truth, by a given system, we need to extend the axiom base in order to prove it. But, this new system also has undecidable propositions, etc., etc..
That is, there is no system of knowledge that is compete in the sense of containing all truths, mathematical or otherwise. (Including God's system if such there be...ie. omniscience is not possible.)

Certainly brains are required to find these new axioms. I don't think that computers can do that, do you?

---------- Post added 12-29-2009 at 06:06 AM ----------



imo,

There is no "Therefore" here at all.

Religious rhetoric is not logic.

Both that is why I placed the thread in the uncategorized forum, also pure philosophy in general depending on the person contributing to the topic, which should go where it wants to go

More!

If you visit the world's largest atheist website, "Infidels", on the home page you will find the following statement:
[CENTER] [/CENTER]
"Naturalism is the hypothesis that the natural world is a closed system, which means that nothing that is not part of the natural world affects it

The digestive system?

How so I beg you?

Endoderm - Wikipedia, the free encyclopedia
Gastrulation - Wikipedia, the free encyclopedia
Gastrulation - Wikipedia, the free encyclopedia
Human gastrointestinal tract - Wikipedia, the free encyclopedia (Primitive gut section)

I tried to read Godel's stuff one time and realized I was going to have to rely on the brains of others in regard to it.

But, the use of the word God to refer to an unknown but required element goes back a long way. Wasn't Aristotle's proofs of God along those lines?

So in other words, this necessary thing is referred to as God. If you don't want to call it that, fine. Since it's unknown, whether it's conscious or not would be speculation.

So, I was wrong. But who made the human gastrointestinal tract? Answer me that! Eh? Eh?

godels theorems are very interesting and profound for sure. Key to his results are the concept of axioms. We start with axioms and build up from there with mathematical systems which we use as models in science. We use different axioms for different mathematical systems, for use in different models. eg real and complex algebra. The axioms cannot be proved within a sufficiently complex system. They can be proved if we extend the system with new axioms, but in doing so we have created an even more complex system, and within that the new axioms cannot be proved.

What we are left with is a choice as to what axioms and mathematical system we use to describe the world.

Suppose then we imagine that we choose an axiomatic mathematical system that describes the behaviour of the physical world. (ie time space energy momentum the lot.) We would still be left with unknowns due to experimental difficulty in confirming the results, but suppose we find no example of the physical world that contradicts the model. Have we found the holy grail of science with a complete theory of matter?

What does it mean that a physical being exists in such a universe that knows that the axioms cannot be proven within that mathematical system, and moreover such a being is able to concieve and mathematically express systems (in writing for example) that are more complex than that scientific mathematical model previously considered complete?

Would the existence and ability of such a being necessarily lead to physical behaviour (in their brain) that is outside the scientific model that was previously considered complete? Because if so then we can always choose to think in a way that creates physical behaviour of matter outside any scientific model we have developed.

But what do we mean by outside the theories of science? The thing to remember is the distinction between a consistent theory and a complete one. It may be concievably possible to develope a mathematical model of the physical world that is never contradicted by scientific experiment....... but that does not make it necessarily complete.

eg a model of football.
The game requires a ball, playing surface, two teams, officials and a set of rules that the officials are responsible to enforce. Officials make mistakes.

There may never be a game that contradicts this description but it is far from complete. Similarly science may develope a theory of matter that is consistent with experiment, but is nevertheless incomplete. There may be all kinds of nuances that are occuring outside the model, but never contradict it.

It may be the case that an experimentally consistent theory of matter based upon a sophisticated mathematical system is found, that nevertheless does not discover any behaviour in the brain that contradicts the theory...... despite the fact that the person being observed experimentally is doing maths that is more complex than the scientific theory and is in that sense outside it.

There is a blastula that precedes the primitive gut... but yeah, infinite regress...

The human gastric system is not a system in isolation, it needs the vagus nerve and brain to function, it needs the liver to metabolize food and so on infinitum

[CENTER]"Anything you can draw a circle around cannot explain itself without referring to something outside the circle - something you have to assume but cannot prove."[/CENTER]

What?

states that:
Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250).

There is no mention of circles or God, here at all.

Your religious nonsense has no relation to Godel's theorems at all.
Give it up, you do not make sese.

---------- Post added 01-20-2010 at 08:33 AM ----------



"Every statement proves its own truth" ??

What?

2+2=4 -> 2+2=4, is not proof of 2+2=4.

Could you explain what you mean here?

Elementary arithmetic does not require any 'infinite' regressions or progressions.

"a system can never be in isolation it always need another system to exist"

How do you know this?

Says who, where and why?

You make a lot of unsupported claims, just for the fun of it, I guess.

well it would seem logical enough but you'd have to obviously make the exception for the base system, then you just get into a sort of cosmological argument

Please!! I only made one claim in my previous post, where do you read a lot of claims?