Re: Godel proved maths inconsistent not incompleteness theorem

On Feb 17, 11:51 pm, "elsiemelsi" <cyprin...@xxxxxxxxxxxxxxx> wrote:
Godel ends up proving maths is inconsistent by useing maths. Godels did not
even prove the incompleteness theorem. The incompleteness theorem is just
an attempt to hide from what he did prove-which is math is inconsistent he
could not accept that so he set up the incompleteness theorem

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf
[quote]Godel proved that mathematics was inconsistent

From Nagel -"Gödel" Routeldeg & Kegan, 1978, p 85-86

***Gödel also showed that G is demonstrable if and only if it's formal
negation ~G is demonstrable.*** However if a formula and its own negation
are both formally demonstrable the mathematical ***calculus is not
consistent*** (this is where he adopts the watered down version noted by
bunch) accordingly if (just assumed to make math's consistent) the
calculus is consistent neither G nor ~G is formally derivable from the
axioms of mathematics. Therefore if mathematics is consistent G is a
formally undecidable formula Gödel then proved that though G is not
formally demonstrable it nevertheless is a true mathematical formula

The mistake isn't in Godel, it is in Bunch. Rosser showed (for his G)
|-G <=> |-~G while Godel proved that G <=> ~|-G.

Actually, there's also a mistake or two by both Godel and Bunch here:

1. Godel didn't prove that G is true using metamathematical means, as
stated by Godel and Bunch. He proved that if the system is sound then
G is true.
2. The wff that expresses "If the system is sound then G is provable"
is provable. Godel himself used a variation of this in his proof of
the second theorem, leaving the odd taste of his saying that we can't
formally prove G but we can formally prove that if the system is
consistent then G is true (thus we cannot prove the system
consistent.) Hopefully this will clear up the confusion. (Just spell
my name right.)

From Bunch
"Mathematical fallacies and paradoxes" Dover 1982" p .151

Including his own! Is there a book of all fallacies made in books of
fallacies (false negatives)? No, by the CBP (C-B Paradox) it is self-
referentially excluded. See http://groups.google.com/group/selfref?hl=en

C-B

Gödel proved

~P(x,y) & Q)g,y)
***in other words ~P(x,y) & Q)g,y) is a mathematical version of the liar
paradox.*** It is a statement X that says X is not provable. ***Therefore
if X is provable it is not provable a contradiction. ***If on the other
hand X is not provable then its situation is more complicated. If X says
it is not provable and it really is not provable then X is true but not
provable ***Rather than accept a self-contradiction mathematicians settle
for the second choice***
[/quote]

[quote]Thus Godel by using invalid axioms and impredicative definitions
only succeeded in getting the inevitable paradox that his axioms and
impredicative definitions ordained him to get. In other words he could
have only ended in paradox for this is what his axioms and impredicative
definitions determined him to get. Thus his proof is a complete failure
as his proof. that mathematics is inconsistent was the only result
that he could have logically arrived at since this result is what his
axioms and impredicative definitions logically would lead him to; because
these axioms and impredicative definitions lead to or end in paradox
themselves. All he succeeded in getting was a paradoxical result..
Godel by using those axioms and impredicative definitions he could only
have arrived at a paradoxical result [/quote]

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