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 Mathematics' Shortcoming? (Kurt Godel)

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PostSubject: Mathematics' Shortcoming? (Kurt Godel)   Wed 18 May 2011, 7:37 pm

First topic message reminder :

By the 1928 international congress of mathematicians Hilbert "made his questions quite precise.
http://en.wikipedia.org/wiki/Turing_machine

+ First, was mathematics complete ...

+ Second, was mathematics consistent ...

+ And thirdly, was mathematics decidable?"
(Hodges p. 91, Hawking p. 1121).


The first two questions were answered in 1930 by Kurt Gödel at the very same meeting where Hilbert delivered his retirement speech (much to the chagrin of Hilbert); the third "the Entscheidungs problem" had to wait until the mid-1930s.

Emil Post developed his definition of a worker moving from room to room writing and erasing marks per a list of instructions (Post 1936), as did Princeton professor Church and his two students Stephen Kleene and J. B. Rosser by use of Church's lambda-calculus and Gödel's recursion theory (1934). Church's paper (published 15 April 1936) showed that the Entscheidungs problem was indeed "undecidable" and beat Turing to the punch by almost a year (Turing's paper submitted 28 May 1936, published January 1937).

Hence, the answer to all three of the above questions is "NO". Funny we didn't learn this in school

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Wed 04 Apr 2012, 12:53 am

ScoutsHonor wrote:
Quote :
Godel's theorem means that the universe cannot be a vast self-contained computer. One modern scientist, Fredekin, suggests that it is.(6) The fundamental particles of nature (in his view) are information bits in that huge machine. Were he right that the universe is effectively a computer, then Godel's theorems would require that nature, as a whole be understood only outside nature because no finite system is sufficient for itself. This conclusion flows by analogy from what Godel proved. "...if arithmetic is consistent, its consistency cannot be established by any meta-mathematical reasoning that can be represented within the formalism of arithmetic."(7)

In my NotSo humble opinion, there is no more reason to postulate that the universe is a computer than that it is a grilled cheese sandwich. What BASIS is there for thinking that?? Didn't the man ever hear of the need for *Evidence*, of some sort...? He sounds very reckless to me.
Computer's can be gamed, in other words they can create a virtual reality that appears to be a "Complete System". This is done via the manipulation of Godel Numbering, which is what computers employ (binanary computing). I'm going to try to do my best to discuss this in the "Why Computers" thread. Anyway, that's why they want the public to believe that the universe is a "computer", for then there doesn't have to be anything 'outside' the system, as Godel showed to the contrary.

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Sun 08 Apr 2012, 8:16 pm

C1 wrote:
ScoutsHonor wrote:
Quote :
Godel's theorem means that the universe cannot be a vast self-contained computer. One modern scientist, Fredekin, suggests that it is.(6) The fundamental particles of nature (in his view) are information bits in that huge machine. Were he right that the universe is effectively a computer, then Godel's theorems would require that nature, as a whole be understood only outside nature because no finite system is sufficient for itself. This conclusion flows by analogy from what Godel proved. "...if arithmetic is consistent, its consistency cannot be established by any meta-mathematical reasoning that can be represented within the formalism of arithmetic."(7)

In my NotSo humble opinion, there is no more reason to postulate that the universe is a computer than that it is a grilled cheese sandwich. What BASIS is there for thinking that?? Didn't the man ever hear of the need for *Evidence*, of some sort...? He sounds very reckless to me.
Computer's can be gamed, in other words they can create a virtual reality that appears to be a "Complete System". This is done via the manipulation of Godel Numbering, which is what computers employ (binanary computing). I'm going to try to do my best to discuss this in the "Why Computers" thread. Anyway, that's why they want the public to believe that the universe is a "computer", for then there doesn't have to be anything 'outside' the system, as Godel showed to the contrary.



I see (well, sort of). I am surprised they care all that much what 'the public' thinks-since their system depends in reality on force; on their established police state. We seem to have evolved from the "fool em" scenario of Brave New World to the "Obey or Else" technique of 1984, which is becoming more and more overt (by way of their "Revelation of the Method" attitudes).
It's also more than possible, though, that they'd rather be able to laugh at us for their ability to fool/deceive us than admit that they have us in chains, and we have no choice.

I've got two words for them, and also I am darn sick and tired of them and their f**ked up existence. !!!
Sorry to have digressed. Sad Will answer the other posts soon as my wrist recovers from this temporary case of fibromyalgia (wrist-soreness) I seem to have developed. Damn!

Talk to you soon (but later). Best. Smile
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Wed 11 Apr 2012, 12:08 am

ScoutsHonor wrote:
I see (well, sort of). I am surprised they care all that much what 'the public' thinks-since their system depends in reality on force; on their established police state. We seem to have evolved from the "fool em" scenario of Brave New World to the "Obey or Else" technique of 1984, which is becoming more and more overt (by way of their "Revelation of the Method" attitudes).
It's also more than possible, though, that they'd rather be able to laugh at us for their ability to fool/deceive us than admit that they have us in chains, and we have no choice.

I've got two words for them, and also I am darn sick and tired of them and their f**ked up existence. !!!
Sorry to have digressed. Sad Will answer the other posts soon as my wrist recovers from this temporary case of fibromyalgia (wrist-soreness) I seem to have developed. Damn!

Talk to you soon (but later). Best. Smile
May I suggest watching, or re-watching, the movie "Monsters, Inc." I think this will answer your question that I've bolded (Remember, the public are the children).

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Sat 14 Apr 2012, 1:53 am

C1 wrote:
ScoutsHonor wrote:
I see (well, sort of). I am surprised they care all that much what 'the public' thinks-since their system depends in reality on force; on their established police state. We seem to have evolved from the "fool em" scenario of Brave New World to the "Obey or Else" technique of 1984, which is becoming more and more overt (by way of their "Revelation of the Method" attitudes).
It's also more than possible, though, that they'd rather be able to laugh at us for their ability to fool/deceive us than admit that they have us in chains, and we have no choice.

I've got two words for them, and also I am darn sick and tired of them and their f**ked up existence. !!!
..Sorry to have digressed. Sad Will answer the other posts soon as my wrist recovers from this temporary case of fibromyalgia (wrist-soreness) I seem to have developed. Damn!

Talk to you soon (but later). Best. Smile
May I suggest watching, or re-watching, the movie "Monsters, Inc." I think this will answer your question that I've bolded (Remember, the public are the children).

I tried to get access to the movie (Monsters, Inc.) but it's no longer available as far as I can tell. Very disappointed about that. BUT, I've copied your dialogue on the subject from the original RPF thread, and it's pasted below. GREAT explanation, C1. Please see my Note at the end, which does contain a question.

========================================
Excerpt from RPF forum thread:
http://www.ronpaulforums.com/showthread.php?204024-Monsters-Inc.-Why-is-this-Pixar-Animiated-Movie-Important -

Interested Participant wrote:

Quote :
This movie shows how the extended media is primarily used to perpetrate fear into the hearts and minds of the public. The Monsters in the movie represent mainstream media, alternative media, Internet media, major nonprofit organization leaders, politicians, etc. (anyone with regular access to the public through authorized channels). The children in the movie are the public at large (children are always used to symbolize the public).

The 3rd-level messaging of this movie is targeted at Insiders (i.e. those that run the system)... and there are two primary purposes of this message:
The first is to mock-the-victim (i.e. the public). The public is mocked by showing them how the system works in cartoon fashion, to reveal the truth right in front of their eyes, using childish imagery. The mockery is complete because the public is too ignorant to see or understand this exoteric message, or to see the blatant mockery. This is typical of psychopathic behavior, where the psychopath must mock the victim as part of their ritual of abuse, as it confirms their power of the victim (ie. public)
The second message is necessary to affirm the system's total domination over the public. If the public is unable to see the exoteric messaging (ie that the system of fear is artificial to maintain fiat power), then the players inside the system remain safe from retribution by the public mob. Hence, the insiders much repeatedly be assured that their systems of control are working, and that the public is not "getting it"... or waking up. Otherwise, the insiders, the controller, would have to quickly adjust their systems of control for fear of being trampled by the mob.

Look for these queues when you watch other movies, or listen to Internet radio. The mocking of the public is everywhere. It's constant, as its an essential feedback into the system of control that's been designed.

============================================
(My note: Is the Third-Level messaging the reason the Globalists are still concerned about keeping the Public fooled? (i.e.." BraveNewWorld vs. ObeyorElse")? Because the public is now thoroughly cowed....so, is it the third level-the "insiders"-that are now the actual & intended target? Hmm.)

pirat



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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Sun 15 Apr 2012, 4:22 pm

ScoutsHonor wrote:
C1 wrote:
ScoutsHonor wrote:
I see (well, sort of). I am surprised they care all that much what 'the public' thinks-since their system depends in reality on force; on their established police state. We seem to have evolved from the "fool em" scenario of Brave New World to the "Obey or Else" technique of 1984, which is becoming more and more overt (by way of their "Revelation of the Method" attitudes).
It's also more than possible, though, that they'd rather be able to laugh at us for their ability to fool/deceive us than admit that they have us in chains, and we have no choice.

I've got two words for them, and also I am darn sick and tired of them and their f**ked up existence. !!!
Sorry to have digressed. Sad Will answer the other posts soon as my wrist recovers from this temporary case of fibromyalgia (wrist-soreness) I seem to have developed. Damn!

Talk to you soon (but later). Best. Smile
May I suggest watching, or re-watching, the movie "Monsters, Inc." I think this will answer your question that I've bolded (Remember, the public are the children).

I tried to get access to the movie (Monster's Inc.) but it's no longer available as far as I can tell. Very disappointed about that. BUT, I've copied your dialogue on the subject from the original RPF thread, and it's pasted below. GREAT explanation, C1. Please see my Note at the end, which does contain a question.

========================================
Excerpt from RPF forum thread:
http://www.ronpaulforums.com/showthread.php?204024-Monsters-Inc.-Why-is-this-Pixar-Animiated-Movie-Important -

Interested Participant wrote:

Quote :
This movie shows how the extended media is primarily used to perpetrate fear into the hearts and minds of the public. The Monsters in the movie represent mainstream media, alternative media, Internet media, major nonprofit organization leaders, politicians, etc. (anyone with regular access to the public through authorized channels). The children in the movie are the public at large (children are always used to symbolize the public).

The 3rd-level messaging of this movie is targeted at Insiders (i.e. those that run the system)... and there are two primary purposes of this message:
The first is to mock-the-victim (i.e. the public). The public is mocked by showing them how the system works in cartoon fashion, to reveal the truth right in front of their eyes, using childish imagery. The mockery is complete because the public is too ignorant to see or understand this exoteric message, or to see the blatant mockery. This is typical of psychopathic behavior, where the psychopath must mock the victim as part of their ritual of abuse, as it confirms their power of the victim (ie. public)
The second message is necessary to affirm the system's total domination over the public. If the public is unable to see the exoteric messaging (ie that the system of fear is artificial to maintain fiat power), then the players inside the system remain safe from retribution by the public mob. Hence, the insiders much repeatedly be assured that their systems of control are working, and that the public is not "getting it"... or waking up. Otherwise, the insiders, the controller, would have to quickly adjust their systems of control for fear of being trampled by the mob.

Look for these queues when you watch other movies, or listen to Internet radio. The mocking of the public is everywhere. It's constant, as its an essential feedback into the system of control that's been designed.

============================================
(My note: Is the Third-Level messaging the reason the Globalists are still concerned about keeping the Public fooled? (i.e.." BraveNewWorld vs. ObeyorElse")? Because the public is now thoroughly cowed....so, is it the third level minions that are now the actual & intended target? Hmm.)

pirat

I think there is an update to that post quoted about Monsters, Inc (the movie), and that is that the Monsters found out that simply trying to frighten the children created only limited amounts of energy, and that the children produced infninitely more energy when made to laugh rather than cry. I believe there is a parallel in the "real" world, in that a public that believes they are free, smart, healthy, etc. will be happiers, less troublesome (for elites) and more "productive". Hence, ultimately, that is why I think it is essential for the system to sell the masses on the Simulacrum.

Also, I think the 3rd level messaging is req'd because it is essential to keep the Technocracy free of fear and happy... for the same reasons that the public must be kept happy - they must keep the Technoracy productive and loyal if the system is going to remain intact.

_________________
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Sun 15 Apr 2012, 7:26 pm

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach to mathematics as the constructive mental activity of humans. That is, mathematics does not consist of analytic activities wherein deep properties of existence are revealed and applied. Instead, logic and mathematics are the application of internally consistent methods to realize more complex mental constructs.

The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. In Brouwer's original intuitionism, the truth of a mathematical statement is a subjective claim: a mathematical statement corresponds to a mental construction, and a mathematician can assert the truth of a statement only by verifying the validity of that construction by intuition.

http://en.wikipedia.org/wiki/Intuitionism

Luitzen Egbertus Jan Brouwer (February 27, 1881 – December 2, 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, a graduate of the University of Amsterdam, who worked in topology, set theory, measure theory and complex analysis.

Brouwer in effect founded the mathematical philosophy of intuitionism as an opponent to the then-prevailing formalism of David Hilbert and his collaborators Paul Bernays, Wilhelm Ackermann, John von Neumann and others (cf. Kleene (1952), p. 46–59). As a variety of constructive mathematics, intuitionism is essentially a philosophy of the foundations of mathematics. It is sometimes and rather simplistically characterized by saying that its adherents refuse to use the law of excluded middle in mathematical reasoning.

Brouwer was member of the Significs group, containing others with a generally neo-Kantian philosophy. It formed part of the early history of semiotics—the study of symbols—around Victoria, Lady Welby in particular. The original meaning of his intuitionism probably can not be completely disentangled from the intellectual milieu of that group.

In 1905, at the age of 24, Brouwer expressed his philosophy of life in a short tract Life, Art and Mysticism described by Davis as "drenched in romantic pessimism" (Davis (2002), p. 94). Schopenhauer had a formative influence on Brouwer, not least because he insisted that all concepts be fundamentally based on sense intuitions. Brouwer then "embarked on a self-righteous campaign to reconstruct mathematical practice from the ground up so as to satisfy his philosophical convictions"; indeed his thesis advisor refused to accept his Chapter II " 'as it stands, ... all interwoven with some kind of pessimism and mystical attitude to life which is not mathematics, nor has anything to do with the foundations of mathematics' " (Davis, p. 94 quoting van Stigt, p. 41). Nevertheless, in 1908:

"... Brouwer, in a paper entitled "The untrustworthiness of the principles of logic", challenged the belief that the rules of the classical logic, which have come down to us essentially from Aristotle (384--322 B.C.) have an absolute validity, independent of the subject matter to which they are applied" (Kleene (1952), p. 46).

http://en.wikipedia.org/wiki/Luitzen_Egbertus_Jan_Brouwer


http://en.wikipedia.org/wiki/Brouwer-Hilbert_controversy
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Thu 19 Apr 2012, 12:45 pm

C1 wrote:
ScoutsHonor wrote:
C1 wrote:
ScoutsHonor wrote:
I see (well, sort of). I am surprised they care all that much what 'the public' thinks-since their system depends in reality on force; on their established police state. We seem to have evolved from the "fool em" scenario of Brave New World to the "Obey or Else" technique of 1984, which is becoming more and more overt (by way of their "Revelation of the Method" attitudes).
It's also more than possible, though, that they'd rather be able to laugh at us for their ability to fool/deceive us than admit that they have us in chains, and we have no choice.

I've got two words for them, and also I am darn sick and tired of them and their f**ked up existence. !!!
..Sorry to have digressed. Sad Will answer the other posts soon as my wrist recovers from this temporary case of fibromyalgia (wrist-soreness) I seem to have developed. Damn!

Talk to you soon (but later). Best. Smile
May I suggest watching, or re-watching, the movie "Monsters, Inc." I think this will answer your question that I've bolded (Remember, the public are the children).

I tried to get access to the movie (Monster's Inc.) but it's no longer available as far as I can tell. Very disappointed about that. BUT, I've copied your dialogue on the subject from the original RPF thread, and it's pasted below. GREAT explanation, C1. Please see my Note at the end, which does contain a question.

========================================
Excerpt from RPF forum thread:
http://www.ronpaulforums.com/showthread.php?204024-Monsters-Inc.-Why-is-this-Pixar-Animiated-Movie-Important -

Interested Participant wrote:

Quote :
This movie shows how the extended media is primarily used to perpetrate fear into the hearts and minds of the public. The Monsters in the movie represent mainstream media, alternative media, Internet media, major nonprofit organization leaders, politicians, etc. (anyone with regular access to the public through authorized channels). The children in the movie are the public at large (children are always used to symbolize the public).

The 3rd-level messaging of this movie is targeted at Insiders (i.e. those that run the system)... and there are two primary purposes of this message:
The first is to mock-the-victim (i.e. the public). The public is mocked by showing them how the system works in cartoon fashion, to reveal the truth right in front of their eyes, using childish imagery. The mockery is complete because the public is too ignorant to see or understand this exoteric message, or to see the blatant mockery. This is typical of psychopathic behavior, where the psychopath must mock the victim as part of their ritual of abuse, as it confirms their power of the victim (ie. public)
The second message is necessary to affirm the system's total domination over the public. If the public is unable to see the exoteric messaging (ie that the system of fear is artificial to maintain fiat power), then the players inside the system remain safe from retribution by the public mob. Hence, the insiders much repeatedly be assured that their systems of control are working, and that the public is not "getting it"... or waking up. Otherwise, the insiders, the controller, would have to quickly adjust their systems of control for fear of being trampled by the mob.

Look for these queues when you watch other movies, or listen to Internet radio. The mocking of the public is everywhere. It's constant, as its an essential feedback into the system of control that's been designed.

============================================
(My note: Is the Third-Level messaging the reason the Globalists are still concerned about keeping the Public fooled? (i.e.." BraveNewWorld vs. ObeyorElse")? Because the public is now thoroughly cowed....so, is it the third level minions-the "Insiders"- that are now the actual & intended target? Hmm.)

pirat

I think there is an update to that post quoted about Monsters, Inc (the movie), and that is that the Monsters found out that simply trying to frighten the children created only limited amounts of energy, and that the children produced infninitely more energy when made to laugh rather than cry. I believe there is a parallel in the "real" world, in that a public that believes they are free, smart, healthy, etc. will be happiers, less troublesome (for elites) and more "productive". Hence, ultimately, that is why I think it is essential for the system to sell the masses on the Simulacrum.

Also, I think the 3rd level messaging is req'd because it is essential to keep the Technocracy free of fear and happy... for the same reasons that the public must be kept happy - they must keep the Technoracy productive and loyal if the system is going to remain intact.

Once one sees it, the ALLEGORY is so striking!! This film, together with "The Matrix" (and no doubt many others) are clear renderings of their modus operandi in the real world. Seeing it so clearly spelled out like that is just...mind-boggling.

My belated reaction..(smile)...to the Matrix. (blush)
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Wed 06 Jun 2012, 1:07 pm

Gödel’s Incompleteness Theorem:
The #1 Mathematical Discovery of the 20th Century
http://www.perrymarshall.com/articles/religion/godels-incompleteness-theorem/

In 1931, Kurt Gödel delivered a devastating blow to the mathematicians of his time
In 1931, the young mathematician Kurt Gödel made a landmark discovery, as powerful as anything Albert Einstein developed.

Gödel’s discovery not only applied to mathematics but literally all branches of science, logic and human knowledge. It has truly earth-shattering implications.

Oddly, few people know anything about it.

Allow me to tell you the story.

Mathematicians love proofs. They were hot and bothered for centuries, because they were unable to PROVE some of the things they knew were true.

So for example if you studied high school Geometry, you’ve done the exercises where you prove all kinds of things about triangles based on a list of theorems.

That high school geometry book is built on Euclid’s five postulates. Everyone knows the postulates are true, but in 2500 years nobody’s figured out a way to prove them.

Yes, it does seem perfectly reasonable that a line can be extended infinitely in both directions, but no one has been able to PROVE that. We can only demonstrate that they are a reasonable, and in fact necessary, set of 5 assumptions.

Towering mathematical geniuses were frustrated for 2000+ years because they couldn’t prove all their theorems. There were many things that were “obviously” true but nobody could figure out a way to prove them.

In the early 1900′s, however, a tremendous sense of optimism began to grow in mathematical circles. The most brilliant mathematicians in the world (like Bertrand Russell, David Hilbert and Ludwig Wittgenstein) were convinced that they were rapidly closing in on a final synthesis.

A unifying “Theory of Everything” that would finally nail down all the loose ends. Mathematics would be complete, bulletproof, airtight, triumphant.

In 1931 this young Austrian mathematician, Kurt Gödel, published a paper that once and for all PROVED that a single Theory Of Everything is actually impossible.

Gödel’s discovery was called “The Incompleteness Theorem.”

If you’ll give me just a few minutes, I’ll explain what it says, how Gödel discovered it, and what it means – in plain, simple English that anyone can understand.

Gödel’s Incompleteness Theorem says:

“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.”

Stated in Formal Language:
 

Gödel’s theorem says: “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, but not provable in the theory.”

The Church-Turing thesis says that a physical system can express elementary arithmetic just as a human can, and that the arithmetic of a Turing Machine (computer) is not provable within the system and is likewise subject to incompleteness.

Any physical system subjected to measurement is capable of expressing elementary arithmetic. (In other words, children can do math by counting their fingers, water flowing into a bucket does integration, and physical systems always give the right answer.)

Therefore the universe is capable of expressing elementary arithmetic and like both mathematics itself and a Turing machine, is incomplete.

Syllogism:

1. All non-trivial computational systems are incomplete

2. The universe is a non-trivial computational system

3. Therefore the universe is incomplete

You can draw a circle around all of the concepts in your high school geometry book. But they’re all built on Euclid’s 5 postulates which are clearly true but cannot be proven. Those 5 postulates are outside the book, outside the circle.

You can draw a circle around a bicycle but the existence of that bicycle relies on a factory that is outside that circle. The bicycle cannot explain itself.

Gödel proved that there are ALWAYS more things that are true than you can prove. Any system of logic or numbers that mathematicians ever came up with will always rest on at least a few unprovable assumptions.

Gödel’s Incompleteness Theorem applies not just to math, but to everything that is subject to the laws of logic. Incompleteness is true in math; it’s equally true in science or language or philosophy.

And: If the universe is mathematical and logical, Incompleteness also applies to the universe.

Gödel created his proof by starting with “The Liar’s Paradox” — which is the statement

“I am lying.”

“I am lying” is self-contradictory, since if it’s true, I’m not a liar, and it’s false; and if it’s false, I am a liar, so it’s true.

So Gödel, in one of the most ingenious moves in the history of math, converted the Liar’s Paradox into a mathematical formula. He proved that any statement requires an external observer.

No statement alone can completely prove itself true.

His Incompleteness Theorem was a devastating blow to the “positivism” of the time. Gödel proved his theorem in black and white and nobody could argue with his logic.

Yet some of his fellow mathematicians went to their graves in denial, believing that somehow or another Gödel must surely be wrong.

He wasn’t wrong. It was really true. There are more things than are true than you can prove.

A “theory of everything” – whether in math, or physics, or philosophy – will never be found. Because it is impossible.

OK, so what does this really mean? Why is this super-important, and not just an interesting geek factoid?

Here’s what it means:

Faith and Reason are not enemies. In fact, the exact opposite is true! One is absolutely necessary for the other to exist. All reasoning ultimately traces back to faith in something that you cannot prove.
All closed systems depend on something outside the system.
You can always draw a bigger circle but there will still be something outside the circle.
Reasoning inward from a larger circle to a smaller circle is “deductive reasoning.”
Example of a deductive reasoning:
1. All men are mortal
2. Socrates is a man
3. Therefore Socrates is mortal

Reasoning outward from a smaller circle to a larger circle is “inductive reasoning.”
Examples of inductive reasoning:

1. All the men I know are mortal
2. Therefore all men are mortal

1. When I let go of objects, they fall
2. Therefore there is a law of gravity that governs falling objects

Notice than when you move from the smaller circle to the larger circle, you have to make assumptions that you cannot 100% prove.

For example you cannot PROVE gravity will always be consistent at all times. You can only observe that it’s consistently true every time. You cannot prove that the universe is rational. You can only observe that mathematical formulas like E=MC^2 do seem to perfectly describe what the universe does.

Nearly all scientific laws are based on inductive reasoning. These laws rest on an assumption that the universe is logical and based on fixed discoverable laws.

You cannot PROVE this. (You can’t prove that the sun will come up tomorrow morning either.) You literally have to take it on faith. In fact most people don’t know that outside the science circle is a philosophy circle. Science is based on philosophical assumptions that you cannot scientifically prove. Actually, the scientific method cannot prove, it can only infer.

(Science originally came from the idea that God made an orderly universe which obeys fixed, discoverable laws.)

Now please consider what happens when we draw the biggest circle possibly can – around the whole universe. (If there are multiple universes, we’re drawing a circle around all of them too):

There has to be something outside that circle. Something which we have to assume but cannot prove
The universe as we know it is finite – finite matter, finite energy, finite space and 13.7 billion years time
The universe is mathematical. Any physical system subjected to measurement performs arithmetic. (You don’t need to know math to do addition – you can use an abacus instead and it will give you the right answer every time.)
The universe (all matter, energy, space and time) cannot explain itself
Whatever is outside the biggest circle is boundless. By definition it is not possible to draw a circle around it.
If we draw a circle around all matter, energy, space and time and apply Gödel’s theorem, then we know what is outside that circle is not matter, is not energy, is not space and is not time. It’s immaterial.
Whatever is outside the biggest circle is not a system – i.e. is not an assemblage of parts. Otherwise we could draw a circle around them. The thing outside the biggest circle is indivisible.
Whatever is outside the biggest circle is an uncaused cause, because you can always draw a circle around an effect.
We can apply the same inductive reasoning to the origin of information:

In the history of the universe we also see the introduction of information, some 3.5 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
All codes we know the origin of are designed by conscious beings.
Therefore whatever is outside the largest circle is a conscious being.
In other words when we add information to the equation, we conclude that not only is the thing outside the biggest circle infinite and immaterial, it is also conscious.

Isn’t it interesting how all these things sound suspiciously similar to how theologians have described God for thousands of years?

So it’s hardly surprising that 80-90% of the people in the world believe in some concept of God. Yes, it’s intuitive to most folks. But Gödel’s theorem indicates it’s also supremely logical. In fact it’s the only position one can take and stay in the realm of reason and logic.

The person who proudly proclaims, “You’re a man of faith, but I’m a man of science” doesn’t understand the roots of science or the nature of knowledge!

Interesting aside…

If you visit the world’s largest atheist website, Infidels, on the home page you will find the following statement:

“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.”

If you know Gödel’s theorem, you know that all logical systems must rely on something outside the system. So according to Gödel’s Incompleteness theorem, the Infidels cannot be correct. If the universe is logical, it has an outside cause.

Thus atheism violates the laws of reason and logic.

Gödel’s Incompleteness Theorem definitively proves that science can never fill its own gaps. We have no choice but to look outside of science for answers.

The Incompleteness of the universe isn’t proof that God exists. But… it IS proof that in order to construct a rational, scientific model of the universe, belief in God is not just 100% logical… it’s necessary.

Euclid’s 5 postulates aren’t formally provable and God is not formally provable either. But… just as you cannot build a coherent system of geometry without Euclid’s 5 postulates, neither can you build a coherent description of the universe without a First Cause and a Source of order.

Thus faith and science are not enemies, but allies. It’s been true for hundreds of years, but in 1931 this skinny young Austrian mathematician named Kurt Gödel proved it.

No time in the history of mankind has faith in God been more reasonable, more logical, or more thoroughly supported by science and mathematics.



“Without mathematics we cannot penetrate deeply into philosophy.
Without philosophy we cannot penetrate deeply into mathematics.
Without both we cannot penetrate deeply into anything.”

-Leibniz

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Wed 06 Jun 2012, 9:10 pm

Thanks for this truly brilliant post, C1.

I am presently marshalling all of my intellectual capacity, and hope to respond with some questions which may shed some more light on this quite difficult issue. Hope I can live up to the level of discussion you've set....but in any event, I will certainly do my best.

I will need to devote some serious time to understanding, or questioning, this Argument (proving the existence of God), so a proper response will undoubtedly take a while longer than I would prefer...(understandably, I guess.)

Also, am wondering if anyone else will have any thoughts on this really fascinating subject. That would be REALLY helpful...well- one can hope, Smile




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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Thu 07 Jun 2012, 1:23 pm

ScoutsHonor wrote:
Thanks for this truly brilliant post, C1.

I am presently marshalling all of my intellectual capacity, and hope to respond with some questions which may shed some more light on this quite difficult issue. Hope I can live up to the level of discussion you've set....but in any event, I will certainly do my best.

I will need to devote some serious time to understanding, or questioning, this Argument (proving the existence of God), so a proper response will undoubtedly take a while longer than I would prefer...(understandably, I guess.)

Also, am wondering if anyone else will have any thoughts on this really fascinating subject. That would be REALLY helpful...well- one can hope, Smile
While Goedel has created an Ontological Proof (proof of God), that I don't think is definitive (I will post on the forum in due time), I believe the greater point that I've been hoping to make is that Man cannot control everything, and therefore can't act as a God. Hence, man can't ultimately control other men. I think that is the greatest significance I've found from Goedel's work.

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Fri 08 Jun 2012, 7:18 am

C1 wrote:
Man cannot control everything, and therefore can't act as a God. Hence, man can't ultimately control other men.

Not only is it impossible for man to control everything, it is fundamentally impossible to completely define or quantify even the simplest aspects of nature, as nature is not merely statistically indeterminate but essentially indeterminate. This essential indeterminacy is that which allows for the validity of concepts like 'soul' or 'free will'.
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Fri 08 Jun 2012, 9:18 pm

mike lewis wrote:
C1 wrote:
Man cannot control everything, and therefore can't act as a God. Hence, man can't ultimately control other men.

Not only is it impossible for man to control everything, it is fundamentally impossible to completely define or quantify even the simplest aspects of nature, as nature is not merely statistically indeterminate but essentially indeterminate. This essential indeterminacy is that which allows for the validity of concepts like 'soul' or 'free will'.

Hi, and welcome to the forum.

I am irresistibly moved to comment (re your comment ^^): That's a very broad statement.. Cool



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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Sat 09 Jun 2012, 12:06 pm

Absolute control of nature maybe out of the question, but ever developing forms and methods of manipulation which are ever increasing in both scope and efficacy is still very much a concern. That is, the manipulators need not achieve omnipotence or omniscience in order to become 'gods' relative to average human beings.
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Sat 09 Jun 2012, 3:52 pm

mike lewis wrote:
Absolute control of nature maybe out of the question, but ever developing forms and methods of manipulation which are ever increasing in both scope and efficacy is still very much a concern. That is, the manipulators need not achieve omnipotence or omniscience in order to become 'gods' relative to average human beings.


Well said. I agree completely. It's not necessary to control all of nature, to control parts of it, and Mankind is indeed vulnerable to those who wield and control untold (technological) power.
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Mon 11 Jun 2012, 2:07 am

ScoutsHonor wrote:
mike lewis wrote:
C1 wrote:
Man cannot control everything, and therefore can't act as a God. Hence, man can't ultimately control other men.

Not only is it impossible for man to control everything, it is fundamentally impossible to completely define or quantify even the simplest aspects of nature, as nature is not merely statistically indeterminate but essentially indeterminate. This essential indeterminacy is that which allows for the validity of concepts like 'soul' or 'free will'.

That's a very broad statement.. Cool

To clarify: To a very significant extant man is a victim of circumstance and a product of his environment, a slave to his own nature and a prisoner to the inherent constraints and limitations intrinsic to the confines of the human condition, this, I think, is self-evident.

I am, however, inclined to think that somewhere within the being of man, beneath or beyond all the deterministic mechanisms and causal operations, is a primitive soul or a proto choice that is not subject to either nature or nurture, heredity or environment.

This implies that at some level of nature the deterministic sequential structure of time and space must cease to apply and Nature's continuum must ultimately be subject to a metaphysical paroxysm. This is what the philosopher Kant referred to as Noumenon.
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Mon 11 Jun 2012, 6:07 pm

mike lewis wrote:
ScoutsHonor wrote:
mike lewis wrote:
C1 wrote:
Man cannot control everything, and therefore can't act as a God. Hence, man can't ultimately control other men.

Not only is it impossible for man to control everything, it is fundamentally impossible to completely define or quantify even the simplest aspects of nature, as nature is not merely statistically indeterminate but essentially indeterminate. This essential indeterminacy is that which allows for the validity of concepts like 'soul' or 'free will'.

That's a very broad statement.. Cool

To clarify: To a very significant extant man is a victim of circumstance and a product of his environment, a slave to his own nature and a prisoner to the inherent constraints and limitations intrinsic to the confines of the human condition, this, I think, is self-evident.

I am, however, inclined to think that somewhere within the being of man, beneath or beyond all the deterministic mechanisms and causal operations, is a primitive soul or a proto choice that is not subject to either nature or nurture, heredity or environment.

This implies that at some level of nature the deterministic sequential structure of time and space must cease to apply and Nature's continuum must ultimately be subject to a metaphysical paroxysm. This is what the philosopher Kant referred to as Noumenon.

This sounds interesting, but Very mystical. I'm afraid I tend to avoid the 'poetic' when it comes to philosophy -- and poetic seems to be an accurate description of Kant's ideas. The reason for this preference is that thinking is a very exacting skill, and requires extremely *precise* (rather than 'poetic') definitions -- if one is going to "get it right." That is, if I'm going to to be successful at understanding the subject, whatever it may be, in clear terms. From what you've quoted, Kant leans strongly towards the mystical/magical. Although I like his attraction to what I would call 'free will' -- which I definitely "believe in" -- it is to me less of an esoteric phenomenon than simply that which man was (happily) naturally endowed with.

Establishing that in essence I would agree with Kant that Noumenon Does exist. Smile

Btw, my own preference philosophically is more towards Ayn Rand's views, by way of Aristotle.Smile Any thoughts about her philosophy?
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Wed 13 Jun 2012, 4:14 pm

ScoutsHonor wrote:
This sounds interesting, but Very mystical. I'm afraid I tend to avoid the 'poetic' when it comes to philosophy -- and poetic seems to be an accurate description of Kant's ideas.


I'm not sure that my statement could be considered "very mystical" or "poetic" by any reasonable person, but no matter, the Universe is a "very mystical" phenomenon whether you or Ayn Rand care to acknowledge it or not.
To demonstrate:





ScoutsHonor wrote:
Btw, my own preference philosophically is more towards Ayn Rand's views, by way of Aristotle.Smile Any thoughts about her philosophy?

Objectivism is not a philosophy. A philosophy must be consistent and non-contradictory. Objectvism is an inconsistent, self contradictory non sequitur which is at odds with both empirical observation and common sense.
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Wed 13 Jun 2012, 4:41 pm

Quote :
The Münchhausen Trilemma (after Baron Münchhausen, who allegedly pulled himself and the horse on which he was sitting out of a swamp by his own hair), also called Agrippa's Trilemma (after Agrippa the Skeptic), is a philosophical term coined to stress the purported impossibility to prove any truth even in the fields of logic and mathematics. It is the name of an argument in the theory of knowledge going back to the German philosopher Hans Albert, and more traditionally, in the name of Agrippa.

If we ask of any knowledge: "How do I know that it's true?", we may provide proof; yet that same question can be asked of the proof, and any subsequent proof. The Münchhausen Trilemma is that we have only three options when providing proof in this situation:

The circular argument, in which theory and proof support each other (i.e. we repeat ourselves at some point)
The regressive argument, in which each proof requires a further proof, ad infinitum (i.e. we just keep giving proofs, presumably forever)
The axiomatic argument, which rests on accepted precepts (i.e. we reach some bedrock assumption or certainty)

The first two methods of reasoning are fundamentally weak, and because the Greek skeptics advocated deep questioning of all accepted values they refused to accept proofs of the third sort. The trilemma, then, is the decision among the three equally unsatisfying options.

In contemporary epistemology, advocates of coherentism are supposed to be accepting the "circular" horn of the trilemma; foundationalists are relying on the axiomatic argument. Not as popular, views that accept (perhaps reluctantly) the infinite regress are branded infinitism.
http://en.wikipedia.org/wiki/M%C3%BCnchhausen_Trilemma
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Tue 26 Jun 2012, 1:26 pm

mike lewis wrote:
ScoutsHonor wrote:
Btw, my own preference philosophically is more towards Ayn Rand's views, by way of Aristotle.Smile Any thoughts about her philosophy?

Objectivism is not a philosophy. A philosophy must be consistent and non-contradictory. Objectvism is an inconsistent, self contradictory non sequitur which is at odds with both empirical observation and common sense.
Well, not to defend Rand, but according to Goedel's proof on incompleteness, isn't every logical man made construct inconsistent?

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Tue 26 Jun 2012, 9:01 pm

C1, wouldnt that apply to Goedel's proof as well? How can Goedel escape his own proof?
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Tue 26 Jun 2012, 11:45 pm

Really good questoin. Somewhere I recall seeing this discussed, but I don't recall the discussion. When/If I find, I'll post.

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Sat 30 Jun 2012, 12:33 am

C1 wrote:

Well, not to defend Rand, but according to Goedel's proof on incompleteness, isn't every logical man made construct inconsistent?

No, Goedel says that either a system is consistent or complete, but cannot be both consistent and complete. If it is complete then it is inconsistent, if it is consistent then it is incomplete.
Quote :
For each consistent formal theory T having the required small amount of number theory, the corresponding Gödel sentence G asserts: "G cannot be proved within the theory T". This interpretation of G leads to the following informal analysis. If G were provable under the axioms and rules of inference of T, then T would have a theorem, G, which effectively contradicts itself, and thus the theory T would be inconsistent. This means that if the theory T is consistent then G cannot be proved within it, and so the theory T is incomplete. Moreover, the claim G makes about its own unprovability is correct. In this sense G is not only unprovable but true, and provability-within-the-theory-T is not the same as truth.

Every logic must by necessity reduce down to axioms or premises, if the premises are true and the logic is sound then the conclusions must be true. Objectivism rests on false premises and then proceeds on unsound logic, therefore it is neither consistent nor complete.
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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Thu 12 Jul 2012, 12:28 pm

An indepth discussionn about Ayn Rand previously started at this point in the thread, and rather than conflate this thread on Goedel, I've relocated all of the posts regarding Rand to its own thread in the Philosophy forum. You may now find that thread at:

http://wwws.forummotion.com/t914-ayn-rand-breakaway-discussion

Thanks

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Thu 12 Jul 2012, 12:43 pm

mike lewis wrote:
C1 wrote:

Well, not to defend Rand, but according to Goedel's proof on incompleteness, isn't every logical man made construct inconsistent?

No, Goedel says that either a system is consistent or complete, but cannot be both consistent and complete. If it is complete then it is inconsistent, if it is consistent then it is incomplete.
Quote :
For each consistent formal theory T having the required small amount of number theory, the corresponding Gödel sentence G asserts: "G cannot be proved within the theory T". This interpretation of G leads to the following informal analysis. If G were provable under the axioms and rules of inference of T, then T would have a theorem, G, which effectively contradicts itself, and thus the theory T would be inconsistent. This means that if the theory T is consistent then G cannot be proved within it, and so the theory T is incomplete. Moreover, the claim G makes about its own unprovability is correct. In this sense G is not only unprovable but true, and provability-within-the-theory-T is not the same as truth.

Every logic must by necessity reduce down to axioms or premises, if the premises are true and the logic is sound then the conclusions must be true. Objectivism rests on false premises and then proceeds on unsound logic, therefore it is neither consistent nor complete.
This highlighted sentence is a very interesting point, and now makes me wonder about the purpose of Gregory Chaitin's work, who has taken Goedel's proof seriously, and now is trying to create an "omega number" that I believe is based on computational probabilities instead of formal set of axioms, which I believe he is doing to 'get around' the completeness limitation (perhaps this thought chain also belongs in the "Why Computers" thread as well).

If you can sit through it, you may find this presentation on Completeness at Google of interest. If you don't want to sit through the entire discussion, then skip to around min 54 (question actually starts at min 53) where a Google employ (rightfully) questions the fact that the presenter thinks that a computational system is more "complete" than an axiomatic system.

Speaker: "more power in computational processes than formal proveability" (ie axiomatic system)



I actually hold out hope because the Google question asker seemed as stumped as I was.

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Tue 04 Dec 2012, 3:56 pm

FYI....Excellent resource for relevant audio material
http://garygeck.com/?page_id=42


``A truly realistic mathematics should be conceived, in line with physics, as a branch of the theoretical construction of the one real world, and should adopt the same sober and cautious attitude toward hypothetic extensions of its foundations as is exhibited by physics.''


~ Hermann Weyl (1949)

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