gimel

it is argued by colin leslie dean that no matter how faultless godels

logic is Godels incompleteness theorem are invalid ie illegitimate

for 5 reasons: he uses the axiom of reducibility- which is invalid ie

illegitimate,he constructs impredicative statement which is invalid ie

illegitimate ,he cant tell us what makes a mathematic statement true,

he falls into two self-contradictions,he ends in three paradoxes

http://www.scribd.com/doc/32970323/Godels-incompleteness-theorem-inva...

http://gamahucherpress.yellowgum.com/gamahucher_press_catalogue.htm

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf

First of the two self-contradictions

Godels first theorem ends in paradox –due to his construction of

impredicative statement

Now the syntactic version of Godels first completeness theorem

reads

 

Proposition VI: To every ω-consistent recursive class c of

formulae there correspond recursive class-signs r, such that neither v

Gen r nor Neg (v Gen r) belongs to Flg© (where v is the free

variable of r).

 

But when this is put into plain words we get

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

 

Gödel's first incompleteness theorem states that:

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).

 

Now truth in mathematics was considered to be if a statement can

be proven then it is true

Ie truth is equated with provability

http://en.wikipedia.org/wiki/Truth#Truth_in_mathematics

 

”…from at least the time of Hilbert's program at the turn of the

twentieth century to the proof of Gödel's theorem and the development

of the Church-Turing thesis in the early part of that century, true

statements in mathematics were generally assumed to be those

statements which are provable in a formal axiomatic system.

The works of Kurt Gödel, Alan Turing, and others shook this

assumption, with the development of statements that are true but

cannot be proven within the system”

 

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

 

“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)

For each consistent formal theory T having the required small

amount of number theory

… provability-within-the-theory-T is not the same as truth; the

theory T is incomplete.”

 

Now it is said godel PROVED

"there are true mathematical statements which cant be proven"

in other words

truth does not equate with proof.

 

if that theorem is true

then his theorem is false

 

PROOF

for if the theorem is true

then truth does equate with proof- as he has given proof of a true

statement

but his theorem says

truth does not equate with proof.

thus a paradox

THIS WHAT COMES OF USING IMPREDICATIVE STATEMENTS

GODEL CAN NOT TELL US WHAT MAKES A STATEMENT TRUE

GODEL CAN NOT TELL US WHAT MAKES A STATEMENT TRUE

Now truth in mathematics was considered to be if a statement can

be proven then it is true

Ie truth was s equated with provability

http://en.wikipedia.org/wiki/Truth#Truth_in_mathematics

 

”…from at least the time of Hilbert's program at the turn of the

twentieth century to the proof of Gödel's theorem and the development

of the Church-Turing thesis in the early part of that century, true

statements in mathematics were generally assumed to be those

statements which are provable in a formal axiomatic system.

 

The works of Kurt Gödel, Alan Turing, and others shook this

assumption, with the development of statements that are true but

cannot be proven within the system”

 

Now the syntactic version of Godels first completeness theorem

reads

Proposition VI: To every ω-consistent recursive class c of

formulae there correspond recursive class-signs r, such that neither v

Gen r nor Neg (v Gen r) belongs to Flg© (where v is the free

variable of r).

 

But when this is put into plain words we get

 

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

 

“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)

 

For each consistent formal theory T having the required small

amount of number theory

… provability-within-the-theory-T is not the same as truth; the

theory T is incomplete.”

 

In other words there are true mathematical statements which cant

be proven

But the fact is Godel cant tell us what makes a mathematical

statement true thus his theorem is meaningless

Ie if Godels theorem said there were gibbly statements that cant

be proven

 

But if godel cant tell us what a gibbly statement was then we

would say his theorem was meaningless

 

Now at the time godel wrote his theorem he had no idea of what

truth was as peter smith the Cambridge expert on Godel admitts

 

http://groups.google.com/group/sci.logi ... 12ee69f0a8

 

Quote:

Gödel didn't rely on the notion

of truth

 

but truth is central to his theorem

as peter smith kindly tellls us

 

http://assets.cambridge.org/97805218...40_excerpt.pdf

Quote:

Godel did is find a general method that enabled him to take any

theory T

strong enough to capture a modest amount of basic arithmetic and

construct a corresponding arithmetical sentence GT which encodes

the claim ‘The sentence GT itself is unprovable in theory T’. So G T

is true if and only

if T can’t prove it

 

If we can locate GT

 

, a Godel sentence for our favourite nicely ax-

iomatized theory of arithmetic T, and can argue that G T is

true-but-unprovable,

 

and godels theorem is

 

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

Quote:

Gödel's first incompleteness theorem, perhaps the single most

celebrated result in mathematical logic, states that:

 

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.

 

you 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

What are you on about? Axioms are always valid by definition, unless they contradict themselves.

read ramsey lips

Ramsey says

 

Such an axiom has no place in mathematics, and anything which cannot be

proved without using it cannot be regarded as proved at all.

 

This axiom there is no reason to suppose true; and if it were true, this

would be a happy accident and not a logical necessity, for it is not a

tautology. (THE FOUNDATIONS OF MATHEMATICS* (1925) by F. P. RAMSEY

and note- he said nothing when godel used it

AND NOTE

Russell following wittgenstien took it out of the 2nd ed due to it being invalid

godel would have know that

russell and wittgenstien new godel used it but said nothing

ramsey points out AR is invalid before godel did his proof

godel would have know ramseys arguments

ramsey would have known godel used AR but said nothing

The Australian philosopher colin leslie dean points out Godels theorem is invalid because it uses invalid axioms ie axiom of reducibility it is the biggest fraud in mathematical history

everything dean has shown was known at the time godel did his proof but no one meantioned any of it

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf

look

godel used the 2nd ed of PM he says

“A. Whitehead and B. Russell, Principia Mathematica, 2nd edition, Cambridge 1925. In particular, we also reckon among the axioms of PM the axiom of infinity (in the form: there exist denumerably many individuals), and the axioms of reducibility and of choice (for all types)”

note he says he is going to use AR

but

Russell following wittgenstien took it out of the 2nd ed due to it being invalid

godel would have know that

russell and wittgenstien new godel used it but said nothing

ramsey points out AR is invalid before godel did his proof

godel would have know ramseys arguments

ramsey would have known godel used AR but said nothing

Ramsey says

 

Such an axiom has no place in mathematics, and anything which cannot be

proved without using it cannot be regarded as proved at all.

 

This axiom there is no reason to suppose true; and if it were true, this

would be a happy accident and not a logical necessity, for it is not a

tautology. (THE FOUNDATIONS OF MATHEMATICS* (1925) by F. P. RAMSEY

every one knew AR was invalid

they all knew godel used it

but nooooooooooooo one said -or has said anything for 76 years untill dean

the theorem is a fraud the way godel presents it in his proof it is crap