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  #1  
Old 01-20-2010, 07:30 AM
nightdreamer nightdreamer is offline
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Godels theorem shown to be invalid ie illegitimate

The Australian philosopher has shown Godels incompletness theorem is invalid for 6 reasons

http://gamahucherpress.yellowgum.com...phy/GODEL5.pdf

.
Quote:
he uses the axiom of reducibility- which is invalid, he uses the axiom of choice, he constructs impredicative statements - which are invalid ,he miss uses the theory of types, he cannot tell us what makes a mathematical statement true, he falls into 3 paradoxes
lets just take deans point that godel cant tell us what makes a mathematical statements true-thus his theorem is meaningless

Godels syntactic proof reads formally

http://en.wikipedia.org/wiki/G%C3%B6...inal_statement
Quote:
"The general result about the existence of undecidable propositions reads as follows:

"Theorem VI. For every ω-consistent recursive class κ of FORMULAS there are recursive CLASS SIGNS r, such that neither v Gen r nor Neg(v Gen r) belongs to Flg(κ) (where v is the FREE VARIABLE of r).[3](van Heijenoort 1967:607.)
but when given meaning word prose

we get
http://en.wikipedia.org/wiki/G%C3%B6...teness_theorem

Quote:
For any consistent formal, recursively enumerable theory that proves
basic arithmetical truths, an arithmetical statement that is true, but not provable in the theory, can be constructed.1 That is, any effectively
generated theory capable of expressing elementary arithmetic cannot be
both consistent and complete.
simply the meaning is
there are true statements which cant be proven
now the cambridge expert on godel Peter smith admits godel did not have a theory of what makes a math statement true
http://gamahucherpress.yellowgum.com...phy/GODEL5.pdf

thus as dean says

Quote:
we see godel referes to true statement
but Gödel didn't rely on the notion
of truth



now because Gödel didn't rely on the notion
of truth he cant tell us what true statements are
thus his theorem is meaningless
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  #2  
Old 01-21-2010, 06:20 AM
Mike Dubbeld Mike Dubbeld is offline
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Hawking and Penrose recognize Godel. But who the hell is nightdreamer? Where can I find your analysis in the Physical Review or some other peer-reviewed publication like Scientific American? Do you have any idea how many people that preceed you that have attempted to trash Godel (and thereby Alan Turing) attempting to have their names forever inscribed in fame by doing so? I think I will pass on your attempt without further proof you are not simply on drugs.
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  #3  
Old 01-21-2010, 06:38 AM
Mike Dubbeld Mike Dubbeld is offline
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You find people attempting to trash Godel by any and all means available simply because if you extend what Godel proved to the human mind you find that the human mind cannot be operating by any such logic (Penrose Shadows of the Mind). The further extension of that is that the AI nuts (which nightdreamer is likely a member) cannot come to grips with the fact that the mind is not simply a Boolean-Turing machine. Machines never will be 'smarter than us'. It puts big fat wrinkle in the poor AI nut's reality. If you can get rid of Godel's Incompletness theorem, you can pave the way for the idea that someday humans will create androids as smart or smarter than humans. But Godel did this long before the words AI (Artificial Intelligence) were even around and no one ever had ever heard words like algorithm and if there was anyone around that knew what a computer program even was, it was likely someone in military intelligence. What Godel proved was it is not possible even in principle to create a set of logical rules (algorithm as per Hilbert's challange) that could be used to explain all of mathematics. Godel showed by contradiction that not only could this never be done but even arithmetic could not be shown to be logically both complete and consistent and therefore anything in mathematics more complex could not be either. It was a major turning point in the history of mathematics. Just like every birdbrain would like to say "Einstein was wrong" view nightdreamer. Big talk but whoever nightdreamer is I don't put him on any sort of par with Hawking and Penrose. I did Godel's proof myself and it is quite convincing when viewed in the proper context. Godel was at the Advanced Institute at the same time as Einstein at Princeton University and they used to walk home together after work and exchange ideas. On a par with Godel in mathematics was the discovery of non-Euclidean geometry.
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  #4  
Old 01-21-2010, 08:48 PM
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PoseidonsNet PoseidonsNet is offline
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there is no formula that can program all the possible mathematical formulae

there is no computer program that can debug all computer programs

there is no computer program that can CREATE any computer program

...
I believe Godel to be correct because

math is quantitative
and always needs to be qualified
by a human (conscious) context

math without language and the qualitative ability to apply it
to the world will never be able to enscribe the complete world

...

its astonishing that herr Dubbeld can understand the subtle complexity of this,
and yet like someone on his first day at phil101
commits the ad hominem argument to try and attack the character
of nightdreamer

I can only conclude the herr Dubbeld,
whilst giving a seemingly logically correct answer,
understands the issue less than nightdreamer does,
whose answer I disagree with,
but whose mind seems more capable of being open to reason.

Herr Dubbeld is a mere parrot.

Godels answer is not based on completely on logic,
its simply based on observing the reality
of what math can and cannot do

math is not creative, its an unchangeable mechanism.

a creative mind can abstract the mechanism
and apply it in any way that logically fits the mechanism

the mind is visionary, imaginative, creative
math
is static

like Mike
__________________
The Principles of Flight (in full)
http://www.poseidons.net/flight/Principlesofflight.htm
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  #5  
Old 03-11-2010, 06:36 AM
nightdreamer nightdreamer is offline
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fact is godel proof is about there being true mathematical statements which cant be proven
as colin leslie dean has shown
godel cant tell us what makes a mathematical statement true
thus his theorem is meaningless babal
ie lets replace true by GIBBLE in the formulation

Quote:
For any consistent formal, recursively enumerable theory that proves
basic arithmetical GIBBLES, an arithmetical statement that is GIBBLES but not provable in the theory, can be constructed.1 That is, any effectively
generated theory capable of expressing elementary arithmetic cannot be
both consistent and complete.
if we are not told what GIBBLES are then the formulation is meaningless nonsense
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  #6  
Old 03-11-2010, 07:12 AM
nightdreamer nightdreamer is offline
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you say
Quote:
Hawking and Penrose recognize Godel
proof from authority is not regarded as a proof-
once most leading thinkers regarded gallelio as wrong
you say

Quote:
I did Godel's proof myself and it is quite convincing when viewed in the proper context
the proof may be faultless
but
as colin leslie dean has shown
the proof is based on an axiom that is regarded as illegitament even by russell himself who abandoned it in his 2 ed of PM -the very edition godel used
ramsey even says AR should be dropped from mathematics
so his theorem for all its logic is illegitament

also even if faultles in its logic
the theorem is meaningless nonsense as godel cant tell us what makes a maths statement true

lets replace true by GIBBLE in the formulation

Quote:
Quote:
For any consistent formal, recursively enumerable theory that proves
basic arithmetical GIBBLES, an arithmetical statement that is GIBBLES but not provable in the theory, can be constructed.1 That is, any effectively
generated theory capable of expressing elementary arithmetic cannot be
both consistent and complete.
if we are not told what GIBBLES are then the formulation is meaningless nonsense
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