Godels incompleteness theorem is proven invalid

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pam69ur
 
Reply Thu 7 Feb, 2008 03:13 am
Godels incompleteness theorem -what he does- is invalid as he uses the invalid axiom the axiom
of reducibility- which Russell Wittgenstein Ramsay and others say is invalid as well as self referencing statements and he falls into 3 paradoxes
What Godel did is invalid
irrespective of what others have done since

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

GODEL'S INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS GODEL IS A COMPLETE FAILURE AS HE ENDS IN UTTER MEANINGLESSNESS
CASE STUDY IN THE MEANINGLESSNESS OF ALL VIEWS
By
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


Take the axiom of reducibility that Godels uses in his proof

Quote:
axiom 1v. (∃u)(v ∀ (u(v) ≡ a))

on substituting for v or u any variables of types n or n + 1 respectively,
and for a a formula which does not contain u free. This axiom represents
the axiom of reducibility
what godel calls the axiom of reducibility is his streamlined version of russells axiom

Quote:
http://www.math.ucla.edu/~asl/bsl/1302/1302-001.ps.

"The system P of footnote 48a is Godel's
streamlined version of Russell's theory of types built on the
natural numbers as individuals, the system used in [1931]. The last
sentence ofthe footnote
allstomindtheotherreferencetosettheoryinthatpaper;
KurtGodel[1931,p. 178] wrote of his comprehension axiom IV, foreshadowing
his approach to set theory, "This axiom plays the role of [Russell's]
axiom of reducibility
(the comprehension axiom of set theory)."
and this axiom is invalid
thus because godel uses it in his proof his proof is invalid


From Kurt Godels collected works vol 3 p.119

Quote:
http://books.google.com/books?id=gD...mSvhA#PPA119,M1

"the axiom of reducibility is generally regarded as the grossest philosophical expediency "



Quote:
from the collected works of godel volume 3
godel states 1939

http://books.google.com/books?id=gD...g=PA119&dq=g...
"to be sure one must observe that the axiom of reducibility appears in
different mathematical systems under different names and forms"

Quote:
the standford encyclopdeia of philosophy says of AR
http://plato.stanford.edu/entries/p...ia-mathematica/

many critics concluded that the axiom of reducibility was simply too ad
hoc to be justified philosophically


Ramsey says

Quote:
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
THUS THE AXIOM IS INVALID ACCORDING TO MOST SCHOLARS
THUS
GODELS THEOREM-WHAT GODEL DID- IS INVALID irrespective of what others have done since


 
Aedes
 
Reply Thu 7 Feb, 2008 12:11 pm
@pam69ur,
"Most" scholars? Russell himself didn't think it was invalid even though he had the most at stake (and he was one of the more arrogant and defensive philosophers of modernity). In fact Russell gave up mathematical logic as a result of Godel's work, and admitted that it's impossible to prove the lack of contradictions in an infinite system, which is a tacit acceptance of Godel.

Furthermore, it's openly acknowledged that Godel's theorem can only apply internally to a system in which proof comes from within the system. This not only absolves Godel's theorem from the critique you raise, but it also shows how it is applicable to mathematics, which is a system whose logic is only derived internally.
 
pam69ur
 
Reply Thu 7 Feb, 2008 06:14 pm
@Aedes,
Quote:
Furthermore, it's openly acknowledged that Godel's theorem can only apply internally to a system in which proof comes from within the system.
What Godel did is invalid as he uses invalid axioms so you cant then say he proved anything


It is a shame the theorem is named after Godel as what Godel proved was invalid. When Dean says Godels theorem is invalid he is refering to what Godel himself did and the theorem that Godel himself proved is invalid

When Godel got his theorem it was the first one on the market and if people had of looked at his proof for the theorem at the time they would have seen it was invalid as he used invalid axioms thus making his theorem invalid

Godel himself proved nothing -irrespective of what others have done- as his proof was based on invalid axioms

You cant say Godel proved this he proved that as he proved nothing as his proof was based on invalid axioms


It maybe
openly acknowledged that Godel's theorem is applicable to systems that is not the point. The point is how Godel proved his theorem is invalid as his proof is invalid thus the theorem he got from his proof is invalid-irrespective of what others have shown or done

As I say its a pity the theorem is named after Godel as what he did is invalid
 
Quatl
 
Reply Thu 7 Feb, 2008 07:31 pm
@pam69ur,
pam69ur wrote:
What Godel did is invalid as he uses invalid axioms so you cant then say he proved anything


There's no path to enlightenment as effective as repetition. I love nothing more than to flog my brain continuously with the same utterance until it is reduced to a fine grey mush.

Please sir/mam I beseech thee: Pummel us about our heads and faces with that sweet, sweet, wisdom until we see the face of god!
 
Aedes
 
Reply Fri 8 Feb, 2008 11:35 am
@pam69ur,
anti
Quote:

Keith Devlin Science, New Series, Vol. 298, No. 5600. (Dec. 6, 2002), pp. 1899-1900.

2.
John W. Dawson, Jr. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1984, Volume Two: Symposia and Invited Papers. (1984), pp. 253-271.

3. What the
Hugh Lacey; Geoffrey Joseph Mind, New Series, Vol. 77, No. 305. (Jan., 1968), pp. 77-83

4.
David Wayne Thomas PMLA, Vol. 110, No. 2. (Mar., 1995), pp. 248-261.

5.
John W. Dawson, Jr.; Cheryl A. Dawson The Bulletin of Symbolic Logic, Vol. 11, No. 2. (Jun., 2005), pp. 150-171.
 
pam69ur
 
Reply Fri 8 Feb, 2008 08:32 pm
@Aedes,
Quote:
i did not say Russell rejected Godel

what I said was Russell abandoned the axiom of reducibility he took it out of 2nd ed PM following - following criticisms of it from Wittgenstein- but Godel still uses it
as he states -

Quote:
"A. Whitehead and B. Russell, Principia Mathematica, 2nd edition, Cambridge 1925. In particular, we also reckon among the axioms of PM the axiom of infinity (in the form: there exist denumerably many individuals), and the axioms of reducibility and of choice (for all types)"
As I say Russell took it out of 2nd ed PM

and AR is considered invalid -then and now
 
 

 
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