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