The Australian philosopher colin leslie dean points out that Godel incompleteness theorem is invalid for a number of reasons :he uses invalid axioms, he constructs self referential statements,he miss uses the theory of types, he falls into internal paradox all of which make his proof invalid -but as dean points out this does not say Godel is wrong only that his proof is invalid

http://gamahucherpress.yellowgum.com/bo ... 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

1) He uses impredicative statements which make his incompleteness theorem invalid

Godel states

“ The solution suggested by Whitehead and Russell, that a proposition

cannot say something about itself , is to drastic... We saw that we can

construct propositions which make statements about themselves,…

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

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

principii) are invalid

even Godel said they make mathematics false

as he states

"consider this rather as a proof that the vicious circle principle is

false than that classical mathematics is false”

It for this reason as well us others ie useing the axiom of reducibility,

paradoxes miss use of the theory of types that colin leslie dean argues

that Godels incompleteness theorem is invalid - irrespective of what

others have proved Godels proof is invalid (being invalid does not mean it

is wrong only that Godels proof is invalid)

2) He uses the axiom of reducibility which make his incompleteness theorem invalid

Godel states about axiom 1v

“this axiom represents the axiom of reducibility (comprehension axiom of

set theory)”

Godel uses axiom 1V the axiom of reducibility in his formula 40 where he

states “x is a formula arising from the axiom schema 1V.1

Russell abandoned this axiom and many beleive it is illegitimant and must

be not used in mathematics

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 )

it for this reason as well us others ie useing impredicative statements

paradoxes miss use of the theory of types that colin leslie dean argues

that Godels incompleteness theorem is invalid - irrespective of what

others have proved Godels proof is invalid (being invalid does not mean

it

## Godels incompleteness theorem proven invalid

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