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Topic: 5 Reasons why Godels incompleteness theorem invalid
Replies: 33   Last Post: Jul 15, 2013 7:20 PM

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 elsiemelsi Posts: 88 Registered: 9/24/07
5 Reasons why Godels incompleteness theorem invalid
Posted: Dec 26, 2007 7:01 AM

The Autralian philosopher Colin Leslie Dean points out Godels theorems are
invalid for 5 reasons: he uses the axiom ofreducibility- which is invalid,
he uses the axiom of choice, he constructs impredicative statements - which
are invalid ,he miss uses the theory of types, he falls into 3 paradoxes

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

GÃDELâS INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS
GÃDEL 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

A case study in the view that all views end in meaninglessness. As an
example of this is GÃ¶delâs incompleteness theorem. GÃ¶del is a complete
failure as he ends in utter meaninglessness. Godels theorems are invalid
for 5 reasons: he uses the axiom of reducibility- which is invalid, he
uses the axiom of choice, he constructs impredicative statements - which
are invalid ,he miss uses the theory of types, he falls into 3 paradoxes

GÃ¶del used impedicative definitions- Russell and Ponicare rejected these

Godel , K , On undecidable propositions of formal mathematical systems, in
The undecidable , M, Davis, Raven Press, 1965, p.63 )

AXIOM OF REDUCIBILITY
(1) Godel uses the axiom of reducibility axiom 1V of his system is the
axiom of reducibility âAs Godel says âthis axiom represents the axiom
of reducibility (comprehension axiom of set theory)â (K Godel , On
formally undecidable propositions of principia mathematica and related
systems in The undecidable , M, Davis, Raven Press, 1965,p.12-13)

. Godel uses axiom 1V the axiom of reducibility in his formula 40 where he
states âx is a formula arising from the axiom schema 1V.1 ((K Godel , On
formally undecidable propositions of principia mathematica and related
systems in The undecidable , M, Davis, Raven Press, 1965,p.21

â [40. R-Ax(x) â¡ (âu,v,y,n)[u, v, y, n <= x & n Var v & (n+1) Var u
& u Fr y & Form(y) & x = u âx {v Gen [[R(u)*E(R(v))] Aeq y]}]

x is a formula derived from the axiom-schema IV, 1 by substitution â
http://www.mrob.com/pub/math/goedel.html

( 2) âAs a corollary, the axiom of reducibility was banished as
irrelevant to mathematics ... The axiom has been regarded as re-instating
http://mind.oxfordjournals.org/cgi/...107/428/823.pdf

2)âdoes this mean the paradoxes are reinstated. The answer seems to be
yes and noâ - http://fds.oup.com/www.oup.co.uk/pdf/0-19-825075-4.pdf )

3) It has been repeatedly pointed out this Axiom obliterates the
distinction according to levels and compromises the vicious-circle
principle in the very specific form stated by Russell. But The philosopher
and logician FrankRamsey (1903-1930) was the first to notice that the axiom
of reducibility in effect collapses the hierarchy of levels, so that the
hierarchy is entirely superfluous in presence of the axiom.
(http://www.helsinki.fi/filosofia/gts/ramsay.pdf)

4) Russell Ramsey and Witgenstein regarded it as illegitimate Russell
abandoned this axiom and many believe it is illegitimate 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

--

Date Subject Author
12/26/07 elsiemelsi
12/26/07 donstockbauer@hotmail.com
12/26/07 Hero
12/26/07 Uncle Archie Relf
12/26/07 David R Tribble
12/27/07 Mark Nudelman
12/27/07 David R Tribble
12/27/07 elsiemelsi
12/27/07 Mark Nudelman
12/27/07 elsiemelsi
12/27/07 elsiemelsi
12/27/07 Porky Pig Jr
12/27/07 elsiemelsi
12/28/07 Mark Nudelman
12/28/07 elsiemelsi
12/28/07 J. Antonio Perez M.
12/28/07 elsiemelsi
12/28/07 Mark Nudelman
12/28/07 elsiemelsi
12/31/07 Mark Nudelman
1/1/08 Aatu Koskensilta
1/1/08 Mark Nudelman
1/2/08 Aatu Koskensilta
7/15/13 Victor
7/15/13 Victor
7/15/13 Victor
7/15/13 Victor
12/28/07 Michel Hack
12/28/07 Hero
12/29/07 Aatu Koskensilta
12/28/07 galathaea
12/28/07 elsiemelsi
12/29/07 Hero
12/30/07 Zim Olson