2 impredicative statements in Godels theorem that invalidate

[das]

Ponicare Russell et al said self referencing statements ie impredicative

definitions are invalid

 

texts books on logic tell us self referencing ,statements (petitio

principii) are invalid

 

Godel uses at least 2 in his incompleteness theorem 1

 

The general result as to the existence of undecidable propositions 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).

 

Godel gives a prof of this

he uses in that proof forumlas 1-45

 

formula 16 is self referencing

 

16. 0 N x ≡ x

 

(n+1) N x ≡ R(3) * n N x

 

note N x appears on both sides of the formular

 

formula 28 which is defined from formular 16 is self referencing

 

28. 0 St v,x ≡ ε n {n <= l(x) & v Fr n,x & not (∃p)[n <=

l(x) & v Fr p,x]}

 

(k+1) St v,x ≡ ε n {n ∃p)[n < p < k St v,x & v Fr p,x]}

 

note St v,x appears on both sides of the formular

 

thus his incompleteness theorem is derived from 2 invalid self referencing

statements and according to colin leslie dean his theorem is thus

invalid

 

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

GÖDEL’S INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS

GÖDEL IS A COMPLETE FAILURE AS HE ENDS IN UTTER MEANINGLESSNESS

CASE STUDY IN THE MEANINGLESSNESS OF ALL VIEWS

By

COLIN LESLIE DEAN

B.SC, B.A, B.LITT (HONS), M.A, B,LITT (HONS), M.A,

M.A (PSYCHOANALYTIC STUDIES), MASTER OF PSYCHOANALYTIC STUDIES, GRAD CERT

(LITERARY STUDIES)

GAMAHUCHER PRESS WEST GEELONG, VICTORIA AUSTRALIA

2007

[Mr Skeptic]

Again, calling it fancy names like begging the question or petitio principii won't make what you say any more true. Self-referring statements are a different beast than circular proofs.

[das]

Self-referring statements are a different beast than circular proofs.

 

formula 16 is self referencing

 

16. 0 N x ≡ x

 

(n+1) N x ≡ R(3) * n N x

 

note N x appears on both sides of the formular

 

note

Nx refers to itself

(n+1) N x ≡ R(3) * n N x

and

is circular

 

Self-referring statements are a different beast than circular proofs.

 

Self-referring statements is a circular statement.

[Mr Skeptic]

Self-referring statements is a circular statement.

 

Exactly. Which is different from a circular proof. Now go learn the difference.

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

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

[das]

stop playing the fool

 

Gödel has offered a rather complex analysis of the vicious circle

principle [self reference] and its devastating effects on classical mathematics culminating

in the conclusion that because it "destroys the derivation of mathematics

from logic, effected by Dedekind and Frege, and a good deal of modern

mathematics itself" he would "consider this rather as a proof that the

vicious circle principle is false than that classical mathematics is

false”

 

We saw that we can construct propositions which make statements about themselves, [i.e self referencing statements or vicious circle] … ((K Godel , On undecidable propositions of formal mathematical systems in The undecidable , M, Davis, Raven Press, 1965, p.63 of this work Dvis notes, “it covers ground quite similar to that covered in Godels orgiinal 1931 paper on undecidability,” p.39.)

 

 

What Godel understood by "propositions which make statements about

themselves"

 

is the sense Russell defined them to be

 

'Whatever involves all of a collection must not be one of the collection.'

Put otherwise, if to define a collection of objects one must use the total

collection itself, then the definition is meaningless. This explanation

given by Russell in 1905 was accepted by Poincare' in 1906, who coined the

term impredicative definition, (Kline's "Mathematics: The Loss of

Certainty"

 

Note Ponicare called these self referencing statements impredicative

definitions

[bascule]

First, your usage of "impredicative" is incorrect, as impredicativity describes the definition of sets, not statements.

 

Second, if you truly want to argue against Godel's theorems, please provide your argument in the form of predicate calculus. If you feel there is something wrong with Godel's self-referential statements, perhaps you could provide a proof which leads to a contradiction and thus demonstrates Godel's arguments to be false.

 

Otherwise, shut the f*ck up already, you annoying troll.

[Big Red Dog]

note

Nx refers to itself

(n+1) N x ≡ R(3) * n N x

and

is circular

 

Self-referring statements is a circular statement.

 

I'm not sure because of this notation but if this is induction you're referring to, one can build consistent and complete system with induction.

 

One more remark:

 

self-reference: you might have noted that Gödel's key set of assertions (those "referencing" themselves) are not referencing directly themselves but rather a property about themselves. Indeed, the "provable" predicate used by Gödel applies to numbers, not to predicate.

 

As to the self references in axioms or mathematical assertions, they are part of the game: x = 2x is just another assertion (say in Arithmetic) that states that x = 0

[Fred56]

shut the f*ck up already, you annoying troll.

...foot on the left pedal, "con passione"

[iNow]

...foot on the left pedal, "con passione"

 

Troll.