Godel makes 2 deceitful moves in his imcompleteness theorem proof

[pam69ur]

the australian philospher colin dean points out that godel makes 2
deceitful moves in his imcompleteness theorem proof

http://gamahucherpress.yellowgum.com...phy/GODEL5.pdf



godels incompleteness theorem reads- note it says to every ω-consistent
recursive class c of formulae



Godel's first Incompleteness Proof at MROB at MROB

Proposition VI: To every ω-consistent recursive class c of formulae there correspond recursive class-signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg(c) (where v is the free variable of r).

now
1) he derives his incompleteness theorem from system P which is made up of
peano and PM but decietfully says it applyies to other system



quote

In the proof of Proposition VI the only properties of the system P
employed were the following:

1. The class of axioms and the rules of inference (i.e. the relation
"immediate consequence of") are recursively definable (as soon as the
basic signs are replaced in any fashion by natural numbers).

2. Every recursive relation is definable in the system P (in the sense of
Proposition V).

Hence in every formal system that satisfies assumptions 1 and 2 and is
ω-consistent, undecidable propositions exist of the form (x) F(x), where
F is a recursively defined property of natural numbers, and so too in
every extension of such

[191]a system made by adding a recursively definable ω-consistent class
of axioms. As can be easily confirmed, the systems which satisfy
assumptions 1 and 2 include the Zermelo-Fraenkel and the v. Neumann axiom systems of set theory,

note his theorem says

to every ω-consistent recursive class c of formulae



but he has only proved his theorem for system P ie PM
so he cant extend that to to every ω-consistent recursive class c of
formulae



he thus trys to decieve us by saying a proof only relevant to system PM is
relevant to every ω-consistent recursive class c of formulae

2 after useing peano and PM in his proof he says



WITHOUT PROOF that footnote 16

16 The addition of the Peano axioms, like all the other changes made in the system PM, serves only to simplify the proof and can in principle be dispensed with.

he has only said that peano and PM can be dropped in any proof after
making his deceitfull extention of his theorem and then

this is deceitfull circular reasoning

in other words
he reasons incorrectly and deceitfully



example



i have used system P to make my proof but my proof is general to other
systems which are not P[WITHOUT PROOF]thus we can drop system P in other
incompleteness proofs [WITHOUT PROOF]

from these decietfull acts people have argued that the system P proof is
only an object proof

but
it is the main proof -as godel tell us



quote

In the proof of Proposition VI the only properties of the system P
employed were the following

and from that proof he gets his incompleteness theorem AND FROM NO WHERE ELSE



THUS GODELS PROOF IS A HOTCHPOTCH OF TRYING TO DECIEVE

[Arjen]

Pam69ur, I hope you realise that every thought based on axioms is curculatory and that therefore every mathematical thought is circulatory. The beautifull thing os mathematics is that the intuitions involved in it stand independent of such axioms. That is why things can be extended to every class of formulae. The recursion takes place because another level is present in our reasoning. All human reasoning has that problem. What is faced there is called a paradox.

Thanks to peano's axioms that is possible in math. It cannot be considered proof though. All we can do is examine the problem of recursion, examine peano's axioms and try to see what is going on. I think in mathematics it will be impossible to prove such a claim as Gödel is trying to prove. We can only conclude that there is incompleteness. My point is that it is not taht Gödel doe snot show the probel, nor that he defines it incorrectly, but the fact that this other "level" cannot be depicted by mathematical formulae unless one takes a different set of axioms for the other "level". In that way this can be understood; although it will create an infinite regress. To make a long story short the infinite regress proves that certain things cannot be depicted in mathematical formulae, but you missed this point.

I'll grant that is cannot be proven in mathematics because of the very same reason though.

I hope this helps..

[Ciana5]

This thread is a perfect example of why we need a forum done in layman`s terms...I had to research way too much of this to fully aprecciate it.
But it does not appear as though Godel was trying to decieve as much as explain something that he did not have all the proper theorim for.
If he had access to the same technology and books we do today, then you`d probably be referencing him instead of this Dean person of whom I have never heard of, nor has the physics professor who is standing over my shoulder.