BOTHERS AND SISTERS, I PRESENT TO YOU Godel's incompleteness theorem

[travellarry]

Hi
this is quiet a solemn topic.
So I'll be very brief and let you think on what I am saying.

The reason this is so important is because it is so simple and sublime. It is profound and earth shattering.

This will give you such a sword in you hand that it will destroy the foundations of any false teacher who opposes the Gospel of our Lord Jesus Christ as taught to us by Apostle Paul, Ray Smith, et. Al.

What I am presenting you brothers and sisters is a tool, is a theorem, is an axiom. It is more presuppositional then Van-Tillian Apologetics.
It is more simple than the simplest of the truths.
Now, I want you guys and gals to pray. Pray with me and let our Good Spirit of our Lord Jesus Christ teach us.
Let our Holy Spirit of God even teach us so much, so that even this what I present now will be refined with fire....

Oh Holy Ghost of our Lord JESUS CHRIST. Please teach us
In JESUS name
Amen

Since this topic is so deep, I will not use any formal system of logical symbols.  I will quote only a article by Douglas Hofstadter who is the Pulitzer-prizewinning author of Gödel, Escher, Bach
It came out in March 1999 in the time magazine.

I WILL NOT PRESENT THE IMPLICATIONS RIGHT NOW. I WANT YOU GUYS TO CHEW THE ARTICLE AND DIGEST IT FOR SOME TIME BEFORE I PRESENT THE IMPLICATIONS.

MY THE GOOD SPIRIT WHO TAUGHT OUR DEAR BROTHER RAY SMITH TEACH US FURTHER.

Kurt Gödel was born in 1906 in Brunn, then part of the Austro-Hungarian Empire and now part of the Czech Republic, to a father who owned a textile factory and had a fondness for logic and reason and a mother who believed in starting her son's education early. By age 10, Gödel was studying math, religion and several languages. By 25 he had produced what many consider the most important result of 20th century mathematics: his famous "incompleteness theorem." Gödel's astonishing and disorienting discovery, published in 1931, proved that nearly a century of effort by the world's greatest mathematicians was doomed to failure.

To appreciate Gödel's theorem, it is crucial to understand how mathematics was perceived at the time. After many centuries of being a typically sloppy human mishmash in which vague intuitions and precise logic coexisted on equal terms, mathematics at the end of the 19th century was finally being shaped up. So-called formal systems were devised (the prime example being Russell and Whitehead's Principia Mathematica) in which theorems, following strict rules of inference, sprout from axioms like limbs from a tree. This process of theorem sprouting had to start somewhere, and that is where the axioms came in: they were the primordial seeds, the Ur-theorems from which all others sprang.
The beauty of this mechanistic vision of mathematics was that it eliminated all need for thought or judgment. As long as the axioms were true statements and as long as the rules of inference were truth preserving, mathematics could not be derailed; falsehoods simply could never creep in. Truth was an automatic hereditary property of theoremhood.
The set of symbols in which statements in formal systems were written generally included, for the sake of clarity, standard numerals, plus signs, parentheses and so forth, but they were not a necessary feature; statements could equally well be built out of icons representing plums, bananas, apples and oranges, or any utterly arbitrary set of chicken scratches, as long as a given chicken scratch always turned up in the proper places and only in such proper places. Mathematical statements in such systems were, it then became apparent, merely precisely structured patterns made up of arbitrary symbols.
Soon it dawned on a few insightful souls, Gödel foremost among them, that this way of looking at things opened up a brand-new branch of mathematics — namely, metamathematics. The familiar methods of mathematical analysis could be brought to bear on the very pattern-sprouting processes that formed the essence of formal systems — of which mathematics itself was supposed to be the primary example. Thus mathematics twists back on itself, like a self-eating snake.

[travellarry]

Bizarre consequences, Gödel showed, come from focusing the lens of mathematics on mathematics itself. One way to make this concrete is to imagine that on some far planet (Mars, let's say) all the symbols used to write math books happen — by some amazing coincidence — to look like our numerals 0 through 9. Thus when Martians discuss in their textbooks a certain famous discovery that we on Earth attribute to Euclid and that we would express as follows: "There are infinitely many prime numbers," what they write down turns out to look like this: "84453298445087 87863070005766619463864545067111." To us it looks like one big 46-digit number. To Martians, however, it is not a number at all but a statement; indeed, to them it declares the infinitude of primes as transparently as that set of 34 letters constituting six words a few lines back does to you and me.

Now imagine that we wanted to talk about the general nature of all theorems of mathematics. If we look in the Martians' textbooks, all such theorems will look to our eyes like mere numbers. And so we might develop an elaborate theory about which numbers could turn up in Martian textbooks and which numbers would never turn up there. Of course we would not really be talking about numbers, but rather about strings of symbols that to us look like numbers. And yet, might it not be easier for us to forget about what these strings of symbols mean to the Martians and just to look at them as plain old numerals?

By such a simple shift of perspective, Gödel wrought deep magic. The Gšdelian trick is to imagine studying what might be called "Martian-producible numbers" (those numbers that are in fact theorems in the Martian textbooks), and to ask questions such as, "Is or is not the number 8030974 Martian-producible (M.P., for short)?" This question means, Will the statement '8030974' ever turn up in a Martian textbook?

Gšdel, in thinking very carefully about this rather surreal scenario, soon realized that the property of being M.P. was not all that different from such familiar notions as "prime number," "odd number" and so forth. Thus earthbound number theorists could, with their standard tools, tackle such questions as, "Which numbers are M.P. numbers, and which are not?" for example, or "Are there infinitely many non-M.P. numbers?" Advanced math textbooks — on Earth, and in principle on Mars as well — might have whole chapters about M.P. numbers.

[travellarry]

And thus, in one of the keenest insights in the history of mathematics, Gödel devised a remarkable statement that said simply, "X is not an M.P. number" where X is the exact number we read when the statement "X is not an M.P. number" is translated into Martian math notation. Think about this for a little while until you get it. Translated into Martian notation, the statement "X is not an M.P. number" will look to us like just some huge string of digits — a very big numeral. But that string of Martian writing is our numeral for the number X (about which the statement itself talks). Talk about twisty; this is really twisty! But twists were Gšdel's specialty — twists in the fabric of space-time, twists in reasoning, twists of all sorts.

By thinking of theorems as patterns of symbols, Gšdel discovered that it is possible for a statement in a formal system not only to talk about itself, but also to deny its own theoremhood. The consequences of this unexpected tangle lurking inside mathematics were rich, mind-boggling and — rather oddly — very sad for the Martians. Why sad? Because the Martians--like Russell and Whitehead — had hoped with all their hearts that their formal system would capture all true statements of mathematics. If Gšdel's statement is true, it is not a theorem in their textbooks and will never, ever show up — because it says it won't! If it did show up in their textbooks, then what it says about itself would be wrong, and who — even on Mars — wants math textbooks that preach falsehoods as if they were true?

The upshot of all this is that the cherished goal of formalization is revealed as chimerical. All formal systems — at least ones that are powerful enough to be of interest — turn out to be incomplete because they are able to express statements that say of themselves that they are unprovable. And that, in a nutshell, is what is meant when it is said that Gödel in 1931 demonstrated the "incompleteness of mathematics." It's not really math itself that is incomplete, but any formal system that attempts to capture all the truths of mathematics in its finite set of axioms and rules. To you that may not come as a shock, but to mathematicians in the 1930s, it upended their entire world view, and math has never been the same since.

Gödel's 1931 article did something else: it invented the theory of recursive functions, which today is the basis of a powerful theory of computing. Indeed, at the heart of Gödel's article lies what can be seen as an elaborate computer program for producing M.P. numbers, and this "program" is written in a formalism that strongly resembles the programming language Lisp, which wasn't invented until nearly 30 years later.

Gšdel the man was every bit as eccentric as his theories. He and his wife Adele, a dancer, fled the Nazis in 1939 and settled at the Institute for Advanced Study in Princeton, where he worked with Einstein. In his later years Gödel grew paranoid about the spread of germs, and he became notorious for compulsively cleaning his eating utensils and wearing ski masks with eye holes wherever he went. He died at age 72 in a Princeton hospital, essentially because he refused to eat. Much as formal systems, thanks to their very power, are doomed to incompleteness, so living beings, thanks to their complexity, are doomed to perish, each in its own unique manner.

[Kat]

Hi Paul,

This is way over my not too mathematically inclined mind.  Maybe somebody else will want to take a stab at this, but I couldn't even read all of it.
Now my head feels like lit's going to explode.

mercy, peace and love
Kat

[eggi]

Hi travellarry,

I didn't get it. I don't see the sword that "will destroy the foundations of any false teacher who opposes the Gospel of our Lord Jesus Christ as taught to us by Apostle Paul, Ray Smith, et. Al."

Could you explain?

God bless you,
Eirik

[travellarry]

brother erik
please ponder, reread and read...i want you to have the full joy of the article by discovering the truth and also the implications of the truth...
please bear my silence, for now
l

[hillsbororiver]

Everything in it's present state is incomplete in the physical Universe. We will only have completeness when God is All in All.

What else could it be? 

Peace,

Joe

[Deborah-Leigh]

Well stated Joe.

Jesus Christ is the "Missing Link".... Nothing incomplete in Him but much in us is not yet completed. Like His image that we are being conformed to.

Peace be to you

Arcturus

[Beloved]

Amen Joe and Arctrus

Travelarry: keep your eyes on Jesus ...he leads us to the Father

God after all is the Great Mathemathician..... men are fools   

Read the end of the article in Time ...Gadel ended up a hypocondriac mumbing to himself. 

Beloved

[John9362]

I'm suprised at you Kat and Eirik............I speed read it and explained it to my 8 and 10 year old daughters all in about 2.38751986521578536884258 minutes, then they explained it to their mother (she was a bit slow).........she took 6.523625877811325 minutes to get it !!...My wife telephoned her 104.5625874525899958752465 year old great grandmother to share this new found knowledge with........... Who inturn explained it to her 88.956321548752335425587 year old daughter.......by now everyone seems to know except you Kat & Eirik ..........I will mention understanding and your names in my prayers  .....LOVE YOU GUYS LOTS !!!!

John


ps.
Actually I'm really 

[eggi]

Ha ha ha!

That's funny John!

I'm glad me and Kat are together in this (and you, according to your PS). I'll try to ponder on it, but I guess I'm still waiting for the explanation!



God bless you,
Eirik

[travellarry]

Very Good Morning Brothers and Sisters, 8:27 eastern, cold and damp here in DC, but one more glorious day from our Lord
Very funny, you guys crack me up. We are complete in Him, In Him dwells all the fullness of Godhead bodily. He is our all in all before God. He is our everything.
Let me be specific to who 'he' is, lest someone say, i'm referring to Godel, hehehehehhe
HE= LORD JESUS CHRIST

The church is the manifold wisdom of God, so even angles try to look into it, to ponder it.(Col, Eph)

Kurt Godel, thou he was very paranoid at the end of his life, is a gift of God to us. That brother (are we not all children of the same father??) of ours is loved by God just as God loves you and me. He is to be respected and his writings should be understood and not feared. God Jesus Christ died for his sins too.

Since Truth cannot be hid, and it comes out through varied places, we have to train our selves to investigate and glory in God's benevolence towards us in giving us Mathematicians and Artists. God is Good.

Now have you guys not learned in schools from unbelievers, is none of your doctor, whom you go when you get sick, are they not many atheists doctors? How come you guys trust them?? How are u sure that the atheists doctors to whom you go for medications do not really hate Christians and they do not want to harm them??

In malice let us be children, and in understanding Men.

Praise our Lord Jesus Christ, let all creation praise him.
l

[Craig]

Larry,

I am not here to say if Godel is right or wrong.  The forum is not the place to bring up others teachings though.  That is not our purpose, our purpose it to discuss the teaching of the scriptures as brought out by Ray smith.

We have allowed some writings of others if a certain statement helps us along our journey, but for the most part other's teachings or theories is not what we are here for, whether they be right or wrong.

Normally your post may be deleted all together, but you are new here and I realize we must learn the ropes.

Hope you understand.


Craig

[travellarry]

Craig
thanks for bearing with me; as an administrator, there is a lot of responsibility you have. and i apologize if i caused any misunderstanding. Please forgive me for that.
Thanks for not deleting my thread.

Let me make some points clearer
Godel's theorem is NOT teaching; neither is it religious sermon. Godel's theorem is not about who Jesus or God or salvation is. That's why it is off topic discussions.

What Godel's theorem IS: Just a tool for apologetics. Godel's theorem is LOGIC. Just as 2+2 is 4 so is Godel's theorem. If 2+2 is teaching, so is Godel's theorem

Hope that lightens up and clears up the discussion.

Peace
l

Larry,

I am not here to say if Godel is right or wrong.  The forum is not the place to bring up others teachings though.  That is not our purpose, our purpose it to discuss the teaching of the scriptures as brought out by Ray smith.

We have allowed some writings of others if a certain statement helps us along our journey, but for the most part other's teachings or theories is not what we are here for, whether they be right or wrong.

Normally your post may be deleted all together, but you are new here and I realize we must learn the ropes.

Hope you understand.


Craig

[travellarry]

alright
before we let this run off having its own life
let me offer some explanation..., this may interest a few...and then we can end this thread

part 1 of godel's theorem: Negative implications
Any system of thought, ANY isms...Like marxism, calvanism, etc.
have a set of basic axioms (something that is true).

now Ingressive axioms are those axioms that go deep into the system, once we attack ingressive axioms and if they prove to be wrong, then we can bring the entire system down.
AND any ism is capable of producing statement that cannot be proved or disproved by the system itself. that is, any system can spew out false statements too

Ex: example in Calvanism: Christ died only for the elect.

Part 2: positive implication
any additional axiom is required to prove a new statement, that cannot be proved with the given set of old axioms

ex: An athetist would say, consistent to his system of axioms: there is no God.
the additional axiom needed to disprove the athetist: there is God.

alright
peace out, lets close this thread.

[Craig]

Larry,

I'm glad you understand the math, but it makes my puny brain hurt  

Math was never my strong point.

Craig

[Kat]

Hi Larry,

But these axioms - a rule or principle widely accepted as obviously true and not needing to be proved, the world is full of these.  It doesn't matter that Ray proves with the Scripture that these axioms are false. 
It is going to take Christ to return and rule with a rod of iron and dispel all these false axioms.
Anyway that's just what I'm thinking.

mercy, peace and love
Kat

[LadyRanae]

The purpose I got from reading about this theorem is...that through the vain imaginings of men.....they "inadvertantly" point to the truth.
If we know 2+2=4...are we complete??
No we are still incomplete without God! 

And so through the "knowledge" of men..they are coming to realize something is missing!!
Praise be to God!

[gmik]

Well, can't say as I understood, but I did like reading this entire thread. It reminded me of the "nothingness" thread.

When we get into math like this or quantim physics, universerse, cell, you name it, the wisdom of man is till folly to God.

But it is interesting at some level.  I am fascinated by the Fibronicci Sequence.  I see God all in that.

[Deborah-Leigh]

The Truth as I know it Travelleary is as Paul states to the Corinthians 2 Chapter 10:5 Inasmuch as we refute arguments and theories and reasoning's and every proud and lofty thing that sets itself up against the true knowledge of God; and we lead every thought and purpose away captive into the obedience of Christ.

It is certainly exciting to learn the laws of nature, maths, science and astronomy but I do believe there should be the balance between worshiping the Creator and not the creation.

I am not knocking the higher echelons of thought and insight into the pursuits of mind in its quest to unlock the secrets of the Universe and the mechanics of life exposed in the pulse of the laws in our Universe. I just know that I am limited in my mind as to the reach and grasp of such matters and prefer other topics of conversation.

It was speculated once that if Einstein married Bay Watch Pamela Anderson that they would produce extraordinary kids. Then it was observed that this was not so because the kids might come out looking like Einstein with the brain power of Pamela!

There are two sides to every coin. It is the face value that counts. Jesus Christ has the highest face value. For me the bottom line is that human knowledge and understanding is the result of Christ,  not the cause of Him or the value of Him. So when I read an article that goes WAY above my head, I realise that while I do not look like Pamela I realise I am not nearly as smart as Einstein and hopefully not as ugly...not yet...

Peace to you

Arcturus