
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
GÃDELâS INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS GÃDEL 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¶delâs 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 as they lead to paradox
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 âAs Godel says âthis 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.1213)
. Godel uses axiom 1V the axiom of reducibility in his formula 40 where he states âx 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. RAx(x) â¡ (âu,v,y,n)[u, v, y, n <= x & n Var v & (n+1) Var u & u Fr y & Form(y) & x = u âx {v Gen [[R(u)*E(R(v))] Aeq y]}]
x is a formula derived from the axiomschema IV, 1 by substitution â http://www.mrob.com/pub/math/goedel.html
( 2) âAs a corollary, the axiom of reducibility was banished as irrelevant to mathematics ... The axiom has been regarded as reinstating the semantic paradoxesâ  http://mind.oxfordjournals.org/cgi/...107/428/823.pdf
2)âdoes this mean the paradoxes are reinstated. The answer seems to be yes and noâ  http://fds.oup.com/www.oup.co.uk/pdf/0198250754.pdf )
3) It has been repeatedly pointed out this Axiom obliterates the distinction according to levels and compromises the viciouscircle principle in the very specific form stated by Russell. But The philosopher and logician FrankRamsey (19031930) 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
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