the australian philospher colin dean points out that godel makes 2

deceitful moves in his imcompleteness theorem proof

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

Quote: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

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

Quote: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

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