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| |-|erc... |
 Posted: Mon Aug 03, 2009 3:39 am |
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Guest
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I did Godel's proof at Uni 20 years ago and it was quite simple. I didn't get it
then my friend stepped me through asking if the formula was true or not, and
whether or not it had a proof and then it must be true, the claim fits the proof
and you get the AHHH feeling, I get it. Everyone in CS theory goes through
the same moment in their lives, passed on from Godel advocate to CS student
throughout modern academic history. But, the proof is a load of sh*t!
You can post it here, and someone will correct you, someone will add their version
then everyone will agree. In 12 months it will be different. According to sci.logic
consensus the wikipedia explanation was accurate, then it was changed by some derelicts
and is wrong. Then the original was not quite right. And it gets more and more complicated
each go, because it's just wrong it's never right. If it was right we'd be using the simple logic
we studied at Uni, but it's just so illogical a whole branch of mathematics that permeates every
facet of knowledge known to man is made_up. Modern mathematics itself was invented to
accomodate Godel's proof, it's that entrenched.
Imagine the sentence, "This sentence makes no sense". Well, who really cares it's just a f*cking
stupid thing to write!! You don't say English language is incomplete because you can make up sh*t!
So why do you do exactly that with mathematics?
If the incompleteness theory was true, then you could prove it by assuming it's not true and see if you
get a contradiction. You don't. The proof follows.
IT (Incompleteness Theorem):
in certain systems there are true statements that are unprovable. (roughly)
Assume ~IT:
~IT = there exists a theory% where all true statements have a proof #
% = a sound recursively enumerable extension of Robinson Arithmetic
let G = G has no proof
Assume G is false
G has no proof is false
G has a proof
G is true
CONTRADICTION
Assume G is true
G has a proof (from #)
G is true
G
G has no proof
CONTRADICTION
G is undecidable ?? (neither true nor false)
IT is not provable from Godel's proof
the incompleteness theorem does not stand up to proof by resolution.
Now, as 1000s of kranks have already tried to tell you, "this has no proof" is EXACTLY the same
class of statment as "this statement is false". We don't invent mathematics to give that the benefit
of the doubt that it's true.
Next week: why "which box contains the numbers of all the boxes that don't contain their own number?"
does NOT mean there are more than infinite boxes. (RE set of all subsets uncountable proof)
Herc
--
Most men are bad, but it takes a women to be evil ~ my mum. |
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| Don Stockbauer... |
| Posted: Fri Aug 07, 2009 2:58 am |
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Guest
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On Aug 3, 4:39 am, "|-|erc" <h... at (no spam) r.c> wrote:
[quote:7fadb03e6c]I did Godel's proof at Uni 20 years ago and it was quite simple. I didn't get it
then my friend stepped me through asking if the formula was true or not, and
whether or not it had a proof and then it must be true, the claim fits the proof
and you get the AHHH feeling, I get it. Everyone in CS theory goes through
the same moment in their lives, passed on from Godel advocate to CS student
throughout modern academic history. But, the proof is a load of sh*t!
You can post it here, and someone will correct you, someone will add their version
then everyone will agree. In 12 months it will be different. According to sci.logic
consensus the wikipedia explanation was accurate, then it was changed by some derelicts
and is wrong. Then the original was not quite right. And it gets more and more complicated
each go, because it's just wrong it's never right. If it was right we'd be using the simple logic
we studied at Uni, but it's just so illogical a whole branch of mathematics that permeates every
facet of knowledge known to man is made_up. Modern mathematics itself was invented to
accomodate Godel's proof, it's that entrenched.
Imagine the sentence, "This sentence makes no sense". Well, who really cares it's just a f*cking
stupid thing to write!! You don't say English language is incomplete because you can make up sh*t!
So why do you do exactly that with mathematics?
If the incompleteness theory was true, then you could prove it by assuming it's not true and see if you
get a contradiction. You don't. The proof follows.
IT (Incompleteness Theorem):
in certain systems there are true statements that are unprovable. (roughly)
Assume ~IT:
~IT = there exists a theory% where all true statements have a proof #
% = a sound recursively enumerable extension of Robinson Arithmetic
let G = G has no proof
Assume G is false
G has no proof is false
G has a proof
G is true
CONTRADICTION
Assume G is true
G has a proof (from #)
G is true
G
G has no proof
CONTRADICTION
G is undecidable ?? (neither true nor false)
IT is not provable from Godel's proof
the incompleteness theorem does not stand up to proof by resolution.
Now, as 1000s of kranks have already tried to tell you, "this has no proof" is EXACTLY the same
class of statment as "this statement is false". We don't invent mathematics to give that the benefit
of the doubt that it's true.
Next week: why "which box contains the numbers of all the boxes that don't contain their own number?"
does NOT mean there are more than infinite boxes. (RE set of all subsets uncountable proof)
Herc
--
Most men are bad, but it takes a women to be evil ~ my mum.
[/quote:7fadb03e6c]
Does the proof have any practical impact on reality? |
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| Marshall... |
| Posted: Fri Aug 07, 2009 5:09 am |
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Guest
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On Aug 7, 6:26 am, "|-|erc" <h... at (no spam) r.c> wrote:
[quote:c26d72afbd]
Now after 100 years, despite rigorous machine checking, 10,000 maths texts,
infallible formal methods, thousands of theorems and new mathematics techniques,
it's really obvious there was an oversight made by Godel.
And the response, does the ball return to Hilbert's side of the court? NO...
"we don't care now"
[/quote:c26d72afbd]
No, that's not the response. The response is "you have failed to
understand the situation."
Marshall |
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| |-|erc... |
| Posted: Fri Aug 07, 2009 7:26 am |
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Guest
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"Don Stockbauer" <donstockbauer at (no spam) hotmail.com> wrote
On Aug 3, 4:39 am, "|-|erc" <h... at (no spam) r.c> wrote:
[quote:ff2833ba06]I did Godel's proof at Uni 20 years ago and it was quite simple. I didn't get it
then my friend stepped me through asking if the formula was true or not, and
whether or not it had a proof and then it must be true, the claim fits the proof
and you get the AHHH feeling, I get it. Everyone in CS theory goes through
the same moment in their lives, passed on from Godel advocate to CS student
throughout modern academic history. But, the proof is a load of sh*t!
You can post it here, and someone will correct you, someone will add their version
then everyone will agree. In 12 months it will be different. According to sci.logic
consensus the wikipedia explanation was accurate, then it was changed by some derelicts
and is wrong. Then the original was not quite right. And it gets more and more complicated
each go, because it's just wrong it's never right. If it was right we'd be using the simple logic
we studied at Uni, but it's just so illogical a whole branch of mathematics that permeates every
facet of knowledge known to man is made_up. Modern mathematics itself was invented to
accomodate Godel's proof, it's that entrenched.
Imagine the sentence, "This sentence makes no sense". Well, who really cares it's just a f*cking
stupid thing to write!! You don't say English language is incomplete because you can make up sh*t!
So why do you do exactly that with mathematics?
If the incompleteness theory was true, then you could prove it by assuming it's not true and see if you
get a contradiction. You don't. The proof follows.
IT (Incompleteness Theorem):
in certain systems there are true statements that are unprovable. (roughly)
Assume ~IT:
~IT = there exists a theory% where all true statements have a proof #
% = a sound recursively enumerable extension of Robinson Arithmetic
let G = G has no proof
Assume G is false
G has no proof is false
G has a proof
G is true
CONTRADICTION
Assume G is true
G has a proof (from #)
G is true
G
G has no proof
CONTRADICTION
G is undecidable ?? (neither true nor false)
IT is not provable from Godel's proof
the incompleteness theorem does not stand up to proof by resolution.
Now, as 1000s of kranks have already tried to tell you, "this has no proof" is EXACTLY the same
class of statment as "this statement is false". We don't invent mathematics to give that the benefit
of the doubt that it's true.
Next week: why "which box contains the numbers of all the boxes that don't contain their own number?"
does NOT mean there are more than infinite boxes. (RE set of all subsets uncountable proof)
Herc
--
Most men are bad, but it takes a women to be evil ~ my mum.
[/quote:ff2833ba06]
Does the proof have any practical impact on reality?
****************************************
I should have expected this one, I'm used to it being the Truman.
Every little thought I have is amplified over a satellite PA and I'm
constantly given feedback on everything I do, vilified more than
anyone else on Earth. Yet when someone else makes an error
and I point it out the mood changes... OVER REACTING, LOOK
TO THE FUTURE NOT THE PAST, FOCUSING ON MISTAKES
So it's funny the adamant proclamations repeated ad nausium what
a profound proof, such a breakthrough that altered the very concepts
of mathematics itself, "this has no proof" looks true yep astounding right there!
Godel showed this, Godel did that, Godel's proof does this. Every thread
about anything to do with formal mathematics after 3 replies... ah but Godel's
result shows this...
Now after 100 years, despite rigorous machine checking, 10,000 maths texts,
infallible formal methods, thousands of theorems and new mathematics techniques,
it's really obvious there was an oversight made by Godel.
And the response, does the ball return to Hilbert's side of the court? NO...
"we don't care now"
As to practical impact, why not, put some more funding into encapsulating mathematics.
Herc |
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| Nick |
| Posted: Fri Aug 07, 2009 10:24 am |
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Joined: 17 Apr 2005
Posts: 3137
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On Aug 7, 7:09 am, Marshall <marshall.spi... at (no spam) gmail.com> wrote:
[quote:37c35c6bf3]On Aug 7, 6:26 am, "|-|erc" <h... at (no spam) r.c> wrote:
Now after 100 years, despite rigorous machine checking, 10,000 maths texts,
infallible formal methods, thousands of theorems and new mathematics techniques,
it's really obvious there was an oversight made by Godel.
And the response, does the ball return to Hilbert's side of the court? NO...
"we don't care now"
No, that's not the response. The response is "you have failed to
understand the situation."
Marshall
[/quote:37c35c6bf3]
If mathmatical axi are multiplying with time Godel is left behind.
What will math be like in a million years let alone science itself?
Mitch Raemsch |
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| herbzet... |
| Posted: Sat Aug 08, 2009 12:32 am |
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Guest
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Don Stockbauer wrote:
[quote:e4050410bd]Does the proof have any practical impact on reality?
[/quote:e4050410bd]
Yes -- it saves mathematicians the labor of futilely looking
for a finitistic completeness proof of number theory and
of theories that extend number theory.
Isn't that handy?
--
hz |
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| Don Stockbauer... |
| Posted: Sat Aug 08, 2009 2:30 am |
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Guest
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On Aug 8, 1:32 am, herbzet <herb... at (no spam) gmail.com> wrote:
[quote:b02e707d31]Don Stockbauer wrote:
Does the proof have any practical impact on reality?
Yes -- it saves mathematicians the labor of futilely looking
for a finitistic completeness proof of number theory and
of theories that extend number theory.
Isn't that handy?
--
hz
[/quote:b02e707d31]
Why do you want them to save their labor? They need some sort of make-
work to fill their lives before they dissociate. |
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| Marshall... |
| Posted: Sat Aug 08, 2009 5:16 am |
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Guest
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On Aug 8, 5:30 am, Don Stockbauer <donstockba... at (no spam) hotmail.com> wrote:
[quote:87095d92ea]On Aug 8, 1:32 am, herbzet <herb... at (no spam) gmail.com> wrote:
Don Stockbauer wrote:
Does the proof have any practical impact on reality?
Yes -- it saves mathematicians the labor of futilely looking
for a finitistic completeness proof of number theory and
of theories that extend number theory.
Isn't that handy?
Why do you want them to save their labor? They need some sort of make-
work to fill their lives before they dissociate.
[/quote:87095d92ea]
Asshole.
Marshall |
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| herbzet... |
| Posted: Sat Aug 08, 2009 7:55 pm |
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Guest
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Don Stockbauer wrote:
[quote:5d481c1ede]herbzet wrote:
Don Stockbauer wrote:
Does the proof have any practical impact on reality?
Yes -- it saves mathematicians the labor of futilely looking
for a finitistic completeness proof of number theory and
of theories that extend number theory.
Isn't that handy?
Why do you want them to save their labor? They need some sort of make-
work to fill their lives before they dissociate.
[/quote:5d481c1ede]
Heh, heh -- don't we all?
I'm guessing they'll find something to keep themselves busy.
--
hz |
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| Don Stockbauer... |
| Posted: Sun Aug 09, 2009 3:08 am |
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Guest
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On Aug 8, 8:55 pm, herbzet <herb... at (no spam) gmail.com> wrote:
[quote:ccaa6c0e44]DonStockbauerwrote:
herbzet wrote:
DonStockbauerwrote:
Does the proof have any practical impact on reality?
Yes -- it saves mathematicians the labor of futilely looking
for a finitistic completeness proof of number theory and
of theories that extend number theory.
Isn't that handy?
Why do you want them to save their labor? They need some sort of make-
work to fill their lives before they dissociate.
Heh, heh -- don't we all?
I'm guessing they'll find something to keep themselves busy.
[/quote:ccaa6c0e44]
Nice thing about free will. You always can.
Godel's proof seems to me to be a highly complex result which is just
sort of "out there" looking for something useful to do. Like a lot of
purely theoretical results.
Perhaps we can equate useful, practical mathematics to garden tools.
Then the Godel sentence might be likened to taking thousands of garden
tools and arranging them into a sentence which can be read from the
air which goes "This sentence is of no use to do actual gardening."
Which is to say that one may contrive a huge complex sentence which
makes a statement, but is useless. But the parts of its substrate
(the simple tools) do have a use.
Yes, I know, such reasoning "is not math".
Sorry about devolving to Marshall's level. I need to work on that. |
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| Don Stockbauer... |
| Posted: Sun Aug 09, 2009 11:23 am |
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Guest
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On Aug 9, 2:22 pm, herbzet <herb... at (no spam) gmail.com> wrote:
[quote:2a7495c890]Don Stockbauer wrote:
herbzet wrote:
Godel's proof seems to me to be a highly complex result which is just
sort of "out there" looking for something useful to do. Like a lot of
purely theoretical results.
Godel's proof(s) have been extremely fruitful mathematically.
You should read up on it. I'm tired of the subject.
[/quote:2a7495c890]
Oh, I have. Notice that "extremely fruitful mathematically" doesn't
pertain to my initial question. And I'm tired of it all, too.
Have a nice day. |
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| herbzet... |
| Posted: Sun Aug 09, 2009 1:22 pm |
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Guest
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Don Stockbauer wrote:
[quote:5d2ed1d89c]herbzet wrote:
Godel's proof seems to me to be a highly complex result which is just
sort of "out there" looking for something useful to do. Like a lot of
purely theoretical results.
[/quote:5d2ed1d89c]
Godel's proof(s) have been extremely fruitful mathematically.
You should read up on it. I'm tired of the subject.
--
hz |
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