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[gimal]

Godel's theorems are invalid for six reasons.

Godel's 1st theorem is about there being true maths statement which cannot be proven. Yet Godel cannot tell us what makes a maths statement true. Thus his theorem is meaningless.

Godel's proof uses his G statement. Yet his G statement is self referential and is banned/outlawed by the axiom of the system he says he is using. Thus his proof is invalid.

To see all the proofs that Godel ends in meaninglessness.
Read.

GODEL’S INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS GODEL IS A COMPLETE FAILURE AS HE ENDS IN UTTER MEANINGLESSNESS
CASE STUDY IN THE MEANINGLESSNESS OF ALL VIEWS

gamahucherpress.yellowgum.com/books/phi ... GODEL5.pdf

-- Updated Sun Oct 23, 2016 3:38 am to add the following --

to give proofs of the two points.

1) Godels theorem in semantic terms reads.

en.wikipedia.org/wiki/G%C3%B6del%27s_in ... ss_theorem

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

but

Peter Smith the Cambridge expert on Godel admitts godel does not tell us what truth is.

peter smith the Cambridge expert on Godel admitts
groups.google.com/group/sci.logic/brows ... 12ee69f0a8



Quote:
Gödel didn't rely on the notion
of truth

thus without telling us what makes a maths statement true Godels theorem is meaningless.


2) Godels G statement is self referential.

en.wikipedia.org/wiki/G%C3%B6del%27s_in ... ss_theorem

“the corresponding Gödel sentence G asserts: “G cannot be proved to be true within the theory T””

Godel uses the axiom of reducibility in his proof.

and as godel states he is useing the logic of PM ie AR

“P is essentially the system obtained by superimposing on the Peano
axioms the logic of PM” ie AR

but.
AR outlaws bans impredicative statements

http://www.enotes.com/topic/Axiom_of_reducibility

russells axiom of reducibility was formed such that impredicative
statements where banned

Thus Godels G statement is self referential and is banned/outlawed by the axiom of the system he says he is using. Thus his proof is invalid.

[Renee]

Charging that Godel did not define "truth" and therefore his theory sucks, is not a valid charge.

Because if you asked for a definition of truth, and Godel gave you one, then you could charge still, demanding definitions of the words which words were used to define truth.

And if the definitions of THOSE words were supplied, you could still say, "This is meaningless, you need to define the words that define the words that define truth." This can go ad infinitum.

So you are starting a recursive process, and declare that the first iteration is missing, therefore the entire recursive process is faulty.

What you are doing is you're denying the power of the language.

Some words don't need to be defined; some words can't be defined, and yet we all agree what they mean.

So nailing Godel to the cross by charging he did not define "truth" is like nailing Jesus to the Cross, for not defining what "King" means in the expression "King of the Jews." (As an example of parallels, nothing more.)

[1i3i6--]

Godel doesn't end in absurdity as many people fail to often understand the difference between a formal and an informal system.
You could seemingly spend an eternity centered on detailing/distinguishing the two.
Suffice to say, Godel provided a brilliant foundation framework for doing so.

To recursively try to iterate or analyze his work is to miss the whole point.

[Renee]

Godel doesn't end in absurdity as many people fail to often understand the difference between a formal and an informal system.

So you say that if someone understands the difference between a formal system and an informal system, then he or she will understand Godel as not ending in absurdity.

I can't agree with that.

[1i3i6--]

Godel doesn't end in absurdity as many people fail to often understand the difference between a formal and an informal system.

So you say that if someone understands the difference between a formal system and an informal system, then he or she will understand Godel as not ending in absurdity.

I can't agree with that.

As you selectively quoted me, Do you agree with :
"To recursively try to iterate or analyze his work is to miss the whole point."
or with :
"You could seemingly spend an eternity centered on detailing/distinguishing the two : Formal/informal system"
?

[ChanceIsChange]

Godel's proof uses his G statement. Yet his G statement is self referential and is banned/outlawed by the axiom of the system he says he is using. Thus his proof is invalid.

The Gödel sentence G refers to itself indirectly. In fact, Gödel proved that such a sentence exists; he did not simply assume its existence. Only in an informal outline is G represented as directly self-referential. Therefore, G is allowed whereas “This sentence is false.” is not (see Wikipedia/Liar Paradox/Gödel's First Incompleteness Theorem).

[Togo1]

Charging that someone who was arguing that all systems are necessarily either incomplete or inconsistent, is being variously incomplete or inconsistent, is missing the point. First off establish that your chosen measures are logically necessary for Godel's theorum to be meaningful, and then, and only then, are we likely to care about whether he meets this arbitrary standard.

[gimal]

to put the point more simple
Godel ends in meaninglessness/contradiction http://gamahucherpress.yellowgum.com/bo ... GODEL5.pdf

Godel's 1st theorem is about there being true math statement which cannot be proven. Yet Godel cannot tell us what makes a mathematics statement true-thus theorem is meaningless

Godel's 1st theorem states "“Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250)" But Godel cannot tell us what makes a mathematics statement true-thus his theorem is meaningless

Also Godel's G statement is banned by the axiom of the system he uses to make his proof-thus his proof cannot go through. Also Godel falls into 2 contradictions and 3 paradoxes-Thus Godel's theorem is meaningless

[Togo1]

to put the point more simple
Godel ends in meaninglessness/contradiction http://gamahucherpress.yellowgum.com/bo ... GODEL5.pdf

Godel's 1st theorem is about there being true math statement which cannot be proven. Yet Godel cannot tell us what makes a mathematics statement true-thus theorem is meaningless

No this doesn't follow. You're mistaking a logical argument (X therefore Y) with a positional argument (I believe X). It doesn't make any difference to Godel's theory what makes a mathematical statement true, merely that it has a truth value.

Godel's 1st theorem states "“Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250)" But Godel cannot tell us what makes a mathematics statement true-thus his theorem is meaningless

Again no, you've missed the point being made. He's demonstrating that a system that proves something true must rely on an unproven axiom. It doesn't matter how or in what way it is proven to be true, merely that there is a truth value.

Your argument is equivalent to arguing that X= 2Y is meaningless because no method is given to derive Y.

[Vodoman]

The universe according to godel is eternity expressing its greation by the use of maths logic. So a rose flower is eternity expressing its self as a rose flower by maths. Am I correct.

[Togo1]

The universe according to godel is eternity expressing its greation by the use of maths logic. So a rose flower is eternity expressing its self as a rose flower by maths. Am I correct.

You may correct about Godel's views, but this isn't what he's famous for.

In general when people talk about Godel's theory they're most often talking about his fundamental incompleteness theorum, which states that any logical system may turn out to be unproveable, even in theory. Prior to Godel there had been a lot of work put into trying to demonstrate a complete thesis of logic, a logical system that would be both proveable and complete. Godel's work holed that project below the waterline, although it was not the only idea that did so.